In the Great Threads model, we found an upper bound on production of any clothing type by calculating the amount that could be produced if all of the resources were devoted to this clothing type. a. What if you instead use a very large value such as 1,000,000 for this upper bound? Try it and see whether you get the same optimal solution. b. Explain why any such upper bound is required. Exactly what role does it play in the model?
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In the Great Threads model, we found an upper bound on production of any clothing type by calculating the amount that could be produced if all of the resources were devoted to this clothing type.
a. What if you instead use a very large value such as 1,000,000 for this upper bound? Try it and see whether you get the same optimal solution.
b. Explain why any such upper bound is required. Exactly what role does it play in the model?
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- 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?The Electro Company manufactures two industrial-sized electrical devices: generators and alternators. Both of these products require wiring and testing during the assembly process. Each generator requires 2 hours of wiring and 1 hour of testing and can be sold for a $250 profit. Each alternator requires 3 hours of wiring time and 140 hours of testing time available in the next production period, and Electro wants to maximize profitIn Excell with show formulas and steps, pleaseWHAT IS THE NEW TOTAL VALUE? A garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2), and chips (x3). The process requires pine bark, machine time, labor time, and storage space. The following model has been developed. Maximize 9x1 + 9x2+ 6x3 (profit) Subject to Bark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutes Labor 2x1 + 4x2 + 3x3 ≤ 480 hours Storage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 What is the new value of the objective function, if the profit on chips increases from $6 per bag to $7 per bag? The New Value Is=
- Andretti Company has a single product called a Dak. The company normally produces and sells 88,000 Daks each year at a selling price of $64 per unit. The company’s unit costs at this level of activity are given below: Direct materials $ 9.50 Direct labor 9.00 Variable manufacturing overhead 2.30 Fixed manufacturing overhead 4.00 ($352,000 total) Variable selling expenses 4.70 Fixed selling expenses 2.50 ($220,000 total) Total cost per unit $ 32.00 A number of questions relating to the production and sale of Daks follow. Each question is independent. Due to a strike in its supplier’s plant, Andretti Company is unable to purchase more material for the production of Daks. The strike is expected to last for two months. Andretti Company has enough material on hand to operate at 25% of normal levels for the two-month period. As an alternative, Andretti could close its plant down entirely for the two months. If the plant were…A goal is to get at least 10% of daily calories from polyunsaturated fats as are found in various nuts, oils, and fish. One serving of walnuts (about 15 pieces) has about 20g of polyunsaturated fat. Each fat gram has 9 calories. About what percent of daily calories does one serving of walnuts provide, assuming a 2,000-calorie diet?A company needs to schedule the monthly production of a certain item for the next 4 months. The unit production cost is estimated to be $12 for the first 2 months and $14 for the last two months. The monthly demands are 750, 1000, 850 and 950 units. The company can increase the monthly production during the second and third months by utilizing overtime. The increase in production by this measure is limited to 400 units per month, and costs an extra $4 per unit. The regular production capacity is 1000 units/month. Excess production can be stored at a cost of $3 per unit per month, but a maximum of 50 units can be stored in any month. Assuming that the beginning and ending inventory levels are zero, formulate this problems as an LP model so that the total cost s minimized.
- Microbrewers Incorporated makes four beers: Light, Dark, Ale, and Premium. The products require: water, malt, hops, and yeast. Assume the supply of water is free, so that it is the amount of other resources that restricts capacity. The following table gives the pound of each resource required in the production of 1 gallon of each product, the pounds of each resource available, and the revenue received for 1 gallon of each product. can you please solve this in excel solver and provide the excel file? Also can you please answer this a. Define the decision variables using complete sentences b. Write down the objective function in words using complete sentences c. Write down the constraints in words using complete sentences d. Express the objective function mathematically using the decision variables defined in part a. e. Express the constraints mathematically using the decision variables defined in part a; see slides for an example.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 $160,000Please complete all work in excel. Use excel to make any necessary calculations and be sure to identify the answer, including units (if necessary). Answers that need formulas must have them within the answer cell. City wants to further develop the model to include the weather conditions of rainy, cloudy, or sunny. Pool Attendance Temperature (°F) Weather Condition 150 89 Sunny 100 82 Rainy 125 81 Cloudy 130 86 Cloudy 155 93 Cloudy 170 98 Sunny 200 99 Sunny 180 87 Sunny 190 88 Sunny 140 83 Sunny 120 82 Cloudy 90 81 Rainy 130 87 Rainy 120 93 Rainy Should you keep weather condition in the model?