Manufacturer firm manufactures two product(X,Y ). Each kg of X requires 5 kWh of electricity and0.25 h of labour. Each kg of Y requires 2 kWh of electricity and 0.5 h of labour. For Y , the quantityof raw materials available permits the maximum production of 60 kg/day. Electricity is limited to 500kWh day and labour to 40 hiday. The X profit is $0,25/kg, while the Y profit is $0,4/kg. To solvethis LP problems by simplex method.there are three basic components must understood:1. Decision variables that seek to determine?2. Formulated the Objective (goal) that need to optimize (maximize or minimize).3. Constraints that the solution must satisfy; and,4. What quantity of cach (X&Y) should be produced and,5. What would the profit be?Activste WindaEإجابتك

First, I would define the decision variables for the above question, here, let me define that total…

Manufacturer firm manufactures two product(X,Y ). Each kg of X requires 5 kWh of electricity and 0,25 h of labour. Each kg of Y requires 2 kWh of electricity and 0.5 h of labour. For Y, the quantity of raw materials available permits the maximum production of 60 kg/day. Electricity is limited to 500 kWh/day and labour to 40 hiday. The X profit is $0.25/kg, while the Y profit is S0.4/kg. To solve this LP problems by simplex method. there are three basie components must understood: 1. Decision variables that seek to determine? 2. Formulated the Objective (goal) that nced to optimize (maximize or minimize). 3. Construints that the solution must satisfy; and, 4. What quantity of cach (X&Y) should be produced and, 5. What would the profit be? Artivate windoe

Manufacturer firm manufactures two product(X,Y ). Each kg of X requires 5 kWh of electricity and 0,25 h of labour. Each kg of Y requires 2 kWh of electricity and 0.5 h of labour. For Y, the quantity of raw materials available permits the maximum production of 60 kg/day. Electricity is limited to 500 kWh/day and labour to 40 hiday. The X profit is $0.25/kg, while the Y profit is S0.4/kg. To solve this LP problems by simplex method. there are three basie components must understood: 1. Decision variables that seek to determine? 2. Formulated the Objective (goal) that nced to optimize (maximize or minimize). 3. Construints that the solution must satisfy; and, 4. What quantity of cach (X&Y) should be produced and, 5. What would the profit be? Artivate windoe

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.4: Fixed-cost Models

Problem 16P

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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?
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
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?
Becton Labs, Inc., produces various chemical compounds for industrial use. One compound, called Fludex, is prepared using an elaborate distilling process. The company has developed standard costs for one unit of Fludex, as follows: Standard Quantityor Hours Standard Priceor Rate Standard Cost Direct materials 2.30 ounces $ 26.00 per ounce $ 59.80 Direct labor 0.50 hours $ 14.00 per hour 7.00 Variable manufacturing overhead 0.50 hours $ 3.40 per hour 1.70 Total standard cost per unit $ 68.50 During November, the following activity was recorded related to the production of Fludex: Materials purchased, 12,500 ounces at a cost of $305,625. There was no beginning inventory of materials; however, at the end of the month, 2,800 ounces of material remained in ending inventory. The company employs 21 lab technicians to work on the production of Fludex. During November, they each worked an average of 150 hours at an average pay rate of $12.00 per hour.…
Wallace Company makes and sells a single product. Each unit of product requires two hours of labor with a wage rate of $8 per hour. The company has budgeted to sell 8,000 units and to produce 10,000 units during the current month. The product requires three pounds of material for each unit produced. Budgeted direct labor costs for the current month would be: $192,000 $128,000 $80,000 $64,000 $160,000
Cantel Company produces cleaning compounds for both commercial and household customers. Some of these products are produced as part of a joint manufacturing process. For example, GR37, a coarse cleaning powder meant for commercial sale, costs $1.90 a pound to make and sells for $2.00 per pound. A portion of the annual production of GR37 is retained for further processing in a separate department where it is combined with several other ingredients to form SilPol, which is sold as a silver polish, at $5.00 per unit. The additional processing requires 1/4 pound of GR37 per unit; additional processing costs amount to $3.90 per unit of SilPol produced. Variable selling costs for SilPol average $0.50 per unit. If production of SilPol were discontinued, $1,000 of costs in the processing department would be avoided. Cantel has, at this point, unlimited demand for, but limited capacity to produce, product GR37. Required: 1. Calculate the minimum number of units of SilPol that would have to be…
Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 11 4 $B$3 Product_2 175 0 25 12 14 $B$4 Product_3 0 −1.5 25 8 5 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 multiple choice Product_1 Product_2 Product_3
Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 10 5 $B$3 Product_2 175 0 25 10 14 $B$4 Product_3 0 −1.5 25 8 6 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 Choose the product Product 1 Product 2 Product 3
Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below. The profit for either model is $1000 per lot. Fliptop Model Tiptop Model Available Plastic 3 4 36 Ink Assembly 5 4 40 Molding Time 5 2 30 Formulate a LP Model for this problem.