The second payment received is:Plot of maximum overdraftS00001200001200001000001000006600081000SP40050000S5000S94001800016200160761500016200-15300153002-18210-2292440206-2247450000440743640661410Overdraft100000Select one:O a. 21600 JD.O b. 43200 JDOc. 16200 JDOd. None of the above.

Name: The second payment received is:Plot of maximum overdraftS000012000012
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Description: The second payment received is:Plot of maximum overdraftS00001200001200001000001000006600081000SP40050000S5000S94001800016200160761500016200-15300153002-18210-2292440206-2247450000440743640661410Overdraft100000Select one:O a. 21600 JD.O b. 43200 JDO

A cost is the resources value in monetary terms spent by the business to produce and deliver the…

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The second payment received is: 1SCO00 Plot of maximum overdraft 120p00 120000 100000 90000 100000 66000 Sepos 59400 61000 81000 59400 50000 55000 18000 16200 16076 15000 16200 -15300 15300 18210 -22924 40206 -22474 50000 4074 36406 -61410 Overdraft -100000 Select one: O a. 21600 JD. O b. 43200 JD Oc. 16200 JD O d. None of the above.

The second payment received is: 1SCO00 Plot of maximum overdraft 120p00 120000 100000 90000 100000 66000 Sepos 59400 61000 81000 59400 50000 55000 18000 16200 16076 15000 16200 -15300 15300 18210 -22924 40206 -22474 50000 4074 36406 -61410 Overdraft -100000 Select one: O a. 21600 JD. O b. 43200 JD Oc. 16200 JD O d. None of the above.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 67P

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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?
SureStep is currently getting 160 regular-time hours from each worker per month. This is actu-ally calculated from 8 hours per day times 20 days per month. For this, they are paid $9.375 per hour(51500y160). Suppose workers can change theircontract so that they only have to work 7.5 hours perday regular-time—everything above this becomesovertime—and their regular-time wage rate increasesto $10 per hour. They will still work 20 days per month. Will this change the optimal no-backloggingsolution?
FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture. Information about the three ingredients (per ounce) is shown below. Ingredient Cost Volume Fat Grams Calories Dried fruit 0.35 0.25 cup 0 150 Nut mix 0.50 0.375 cup 10 400 Cereal mix 0.20 1 cup 1 50 Let D = number of ounces of dried fruit mix in the blend; N = number of ounces of nut mix in the blend ; C = number of ounces of cereal mix in the blend. The constraint that would ensure the mixture has no more than 25 grams of fat is:
Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.
The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both rquire a certain amount of wiring and drilling. Each air condtioner takes 3 hours of wiring and 2 hours of drilling. During the next production period, 240 hours of wiring time are available, and up to 140 hours of drilling time may be used. Each air conditioner sold yieds a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate the best combination of air conditioners and fans that yiedls the highest profit. Use the corner point graphical approach.
Type the linear program, optimal solution, and objective function value in a word document. Submit your excel file A company produces three different types of wrenches: W1, W2, and W3. It has a firm order for 2,000 W1 wrenches, 3,750 W2 wrenches, and 1,850 W3 wrenches. Between now and the delivery date, the company has only 17,500 fabrication hours and 1,600 inspection hours. The time that each wrench requires in each department is shown in the table for this problem. Also shown are the costs to manufacture the wrenches in-house and the costs to outsource them. For labelling considerations, the company wants to manufacture in-house at least 60% of each type of wrench that will be shipped. How many wrenches should be outsourced? What will be the total cost to satisfy the order? Wrench Fabrication Hours Inspection Hours In-House Cost Outsource Cost W1 2.25 0.25 $17.00 $19.00 W2 3.25 0.30 $19.00 $21.00 W3 3.75 0.45 $22.00 $24.00
1.) Objective Function: Maximize Z = 60X₁ +50X₂ Subject to Assembly 4X₁ + 10X ₂ ≤ 100 hours Inspection 2X₁ + 1X₂ ≤ 22 hours Storage 3X ₁ + 3X₂ ≤ 39 cubic feet X₁, X₂ ≤ 0Solve the following completely by graphical method:a) corner point methodb) iso profit line 2.) Suppose, 240 acres of land available.Profit: $40/acres corn: $30/acre oats Have 320 hours of labor available.Corn takes 2 hours of labor per acre of land; however, Oats requires 1 hour of labor per acre of land. Problem: How many acres of each should be planted to maximize profit? a) Formulate the problem.b) Solve the problem using graphical method (corner point solution) and Iso profit method.
Use two phase method for solving Maximize: Z = 4X1 + 3X2 + 9X3 Subject to: 2X1 + 4X2 + 6X3 ≥ 15 6X1 + X2 + 6X3 ≥ 12 X1, X2, X3 ≥ 0
The ABC Company manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 375 hours of wiring time are available and up to 180 hours of drilling time may be used. Each air conditioner sold yields a profit of $35. Each fan assembled may be sold for a $25 profit. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graphical approach. a. How many air conditioners should be produced to get the maximized profit? b. How many fans should be produced to get the maximized profit? c. How much is the maximized profit?