The Ace Manufacturing Company has orders for three similar products.Orders(units)ProductABс12Machine3AThree machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending onthe machine used. Machine capacities for the next week and the unit costs are shown below.ABBICcсProduct122,20033001,400Capacity(units)1,8001,7008001Machine23$1.00 $1.30 $1.10$1.20 $1.40 $1.00$0.90 $1.20 $1.20 (a) Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, x; be the number of units of product i produced by machine j, etc.)X₁Min 1x14 +1.3x1B + 1.1x10+1.2x24 +1.4x2B + 1x2c +0.9x34 +1.2x3B+1.2x30Check which variable(s) should be in your answer.s.t.Machine 1 CapacityMachine 2 CapacityMachine 3 CapacityProduct A OrdersProduct B OrdersProduct C Orders1x14+ 1x1B + 1x1C ≤ 1800XCheck which variable(s) should be in your answer.1x24 + 1x2B + 1x2C≤1700XCheck which variable(s) should be in your answer.1x24+ 1x2B + 1x₂C≤800XCheck which variable(s) should be in your answer.*14+*24+x34 = 2200XCheck which variable(s) should be in your answer.|X1B+X2B+X3B = 300XCheck which variable(s) should be in your answer.|*1c+x₂c + x3c=1400|XCheck which variable(s) should be in your answer.XX¡i¡ 2 0 for all i, j.(b) Solve the transportation model for the minimum cost production schedule for the products and machines.Show the production schedule.(XA1¹ XA2¹ ×A3¹ ×81¹ ×82¹ ×83¹ ×C1₁¹ *c2′ Xc3) = ( 1400,300,0,0,0,1400,800,0,0 |x)Determine the cost (in dollars) of the production schedule.Total = $ 3910X

Linear Programming is an optimization method to determine the best outcome or optimal solution out…

Answered: (a) Develop the linear programming…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 33P: Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand...

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Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
Triple X Company manufactures and sells refrigerators. It makes some of the parts for the refrigerators and purchases others. The engineering department believes it might be possible to cut costs by manufacturing one of the parts currently being purchased for $8.25 each. The fi rm uses 100,000 of these parts each year. The accounting department compiles the following list of costs based on engineering estimates:Fixed costs will increase by $50,000. Labor costs will increase by $125,000.Factory overhead, currently running $500,000 per year, may be expected to increase 12 percent.Raw materials used to make the part will cost $600,000.Given the preceding estimates, should Triple X make the part or continue to buy it?
I need a detailed assistance to solve this problem in: Operations Analysis. #4) A greengrocer has exactly 1,000 square feet available to display and sells 3 kinds of vegetables. The space consumed by each kind of vegetable is proportional to its cost, and tomatoes consume 0.5 square feet per pound. There is a $100 setup cost for replenishing any of the vegetables, and the interest rate is 25% per annum. The 3 vegetables for sale have the following data: Tomatoes: annual demand is 850 pounds and the cost per pound is $0.29. Lettuce: annual demand is 1280 pounds and the cost per pound is $0.45. Zucchini: annual demand is 630 pounds and the cost per pound is $0.25. a) - What is the optimal quantity for purchasing each vegetable (include all formulas)?
Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rod is $2,000, and the cost required to set up the production for the 6-cylinder connecting rod is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line.Once the line has been set up, the weekly production capacities are 6,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Letx4 = the number of 4-cylinder connecting rods produced next week,x6 = the number of 6-cylinder connecting rods produced next week,s4 = 1 if the production line is set up to produce the 4-cylinder…
Telsla produces a range of electric car models. The following presents hypothetical information in regards to the production of these cars. The production manager would like your assistance to identify the optimal production mix. Below is an estimation of the costs to manufacture these products. Model S Model 3 Model X Selling price $130,000.00 $63,000.00 $150,000.00 Direct materials $60,000.00 $26,000.00 $67,000.00 Direct labour $17,500.00 $11,500.00 $20,750.00 Variable overhead $13,125.00 $8,625.00 $15,562.50 Fixed overhead $8,750.00 $5,750.00 $10,375.00 Each of these products goes through the same manufacturing process. The time for each process required for each model and the total hours available for each process are provided in the table below. Process Model S Model 3 Model X Total hours available Body 2 1.5 2.5 750,000 Stamping 1 0.75 1.2 400,000 Plastics 2 1.75 2.1 700,000 Assembly 4 3.5 4.5 1,400,000 Required: Using Excel…
The Crandon Manufacturing Company produces two principal product lines. One is a portable circular saw, and the other is a precision table saw. Two basic operations are crucial to the output of these saws: fabrication and assembly. The maximum fabrication capacity is 4000 hours per month; each circular saw requires 2 hours, and each table saw requires 1 hour. The maximum assembly capacity is 5000 hours per month; each circular saw requires 1 hour, and each table saw requires 2 hours. The marketing department estimates that the maximum market demand next year is 3500 saws per month for both products. The average contribution to profits and overhead is $900 for each circular saw and $600 for each table saw. Management wants to determine the best product mix for the next year so as to maximize contribution to profits and overhead. Also, it is interested in the payoff of expanding capacity or increasing market share.
A carpenter produces chairs, tables, and windows. The following information is provided: Cost of production per unit of chairs, tables, and windows is 2, 4, and 6 respectively, and can be sold at 7, 10, and 12, respectively. Weekly demand on chairs, tables, and windows is expected to not exceed 400, 200, and 100, respectively. Production of the three products requires wood, metal sheets and paint. The following table shows the unit requirement of each of the three materials needed and the availability of each. Chairs Tables Windows Weekly availability Wood 2 3 7 1000 Metal Sheets 1 - 1 400 Paint 3 5 10 2000 Production of tables may not exceed twice the units produced of chairs. Total production budget is expected to be 10,000 Pounds every week. Formulate the linear programming model to determine the number of units to produce of the three products such that the net profit is maximized.

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