MATH451-Unit 2 Intellipath - Make Buy Decision
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MATH451 – Unit 2 Intellipath
Make-Buy Decision
Sometimes it becomes either necessary or beneficial to outsource some of the demands to another company. In this case, you need to make a decision to how many of each order has to be done in house (make) and the remaining of the order be performed by the outsource vendor. In this section, you will revise a linear programming model and compare the results.
In this section, you will be presented an original scenario. You will then revise
the model based on the new scenario. If you are already familiar with the original scenario, you may move onto the section called
Revised Scenario
.
Original Scenario
You are in a business of making chairs, tables, and desks at a company called Allen Furniture. You sell each chair for $120, table for $150, and desk for $200. Each chair, table, and desk consumes 8.5, 10 and 14.5 square feet of lumber; 1, 1.5, and 2 hours of labor; and finally 4, 5, and 6 pounds of screws, respectively. You need to deliver at most 950 chairs, at most 800 tables, and at least 400 desks. You have a total of 14,000 square feet of lumber, 2,000 hours of labor, and 6,000 pounds of screws.
The objective function and the constraints are as follows:
Maximizing revenue = $120C + $150T + $200D
subject to
8.5C + 10T + 14.5D ≤ 14,000 square feet of lumber
1C + 1.5T + 2D ≤ 2,000 hours of labor
4C + 5T + 6D ≤ 6,000 pounds of screws
C ≤ 950, T ≤ 800, D ≥ 400 units
C, T, and D ≥ 0 (nonnegativity)
Results of the Original Scenario
Using the Excel’s Solver program to the run the linear programming model, you will produce a feasible region with the optimal solution of 0 chair, 240 tables, and 800 desks. The profit was maximized for $196,000.
Revised Scenario
It is hard to imagine why a company wants to involve another vendor(s) to perform the functions that it can easily do and collect all the revenue rather than sharing the revenue. Due to competition it may be financially beneficial to allow another vendor(s) to become your partner to produce some of your orders. You revise Allen Furniture by allowing Mike’s Furniture Company to provide some of the chairs, tables, and desk you are trying to make.
Setting Up the New Linear Programming Model
Suppose Mike’s Furniture Company has sufficient surplus to fill the entire order or part of the order taken by Allen Furniture. Also assume that you need to satisfy all demand exactly. Mike’s Furniture Company charges Allen Furniture store $100, $110, and $160 for any chair, table, and desk, respectively.
The objective function and the constraints are as follows:
Maximizing revenue = $120C + $150T + $200D − ($100CM + $110TM + $160DM)
subject to
8.5C + 10T + 14.5D ≤ 14,000 square feet of lumber
1C + 1.5T + 2D ≤ 2,000 hours of labor
4C + 5T + 6D ≤ 6,000 pounds of screws
C = 950, T = 800, D = 400 units
C, T, and D ≥ 0 (nonnegativity)
where CM, TM, and DM are those chairs, tables, and desks made by Mike’s Furniture Company and C, T, and D are those made by both.
Figure 1 shows the Excel’s Solver program used to solve the linear programming model containing all of the required excel functions.
Figure 1:
Excel’s Solver Program Used to Solve the Linear Programming Model
Figure 2 shows the same program containing the numerical values of the decision-making variables and the amount of resources consumed.
Figure 2:
Results of the Application Using Excel’s Solver
Results of the Revised Scenario
As you can see from the results, 900 chairs, 0 table, and 400 desks were made by Allen Furniture and the remaining 50 chairs, 800 tables, and 0 desks were made by Mike’s Furniture Company. The revenue was maximized
to $221,00 which is $25,000 more in revenue than previous example’s value.
You also noticed that Allen Furniture could not handle such a large order by himself due to his restriction of resources. Partnership with Mike’s Furniture
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Company not only helped Allen to complete the order, but also brought $3,000 more revenue for Allen.
Q:
Allen Furniture needs to produce 700 chairs, 300 tables, and 200 desks to fill an order. It has 10,000 square feet of lumber, 1,500 hours of production time, and 3,000 pounds of hardware available. It outsources part of the production to Mike's Furniture Company. The solution produced by Excel's Solver is given below.
The optimal solution results in a maximum revenue of _______?
A:
$137,600
Q:
Allen Furniture needs to produce 750 chairs, 350 tables, and 150 desks to fill an order. It has 12,000 square feet of lumber, 1,800 hours of production time, and 4,000 pounds of screws available. It outsources part of the production to Mike's Furniture Company. The solution produced by Excel's Solver is given below. Based on the given output by Solver, which of the following statements is true?
A:
Mike's Furniture Company charges Allen Furniture $110 for each chair. OR Mike's Furniture Company charges Allen Furniture $115 for each table. OR
There will be a surplus of lumber with the optimal solution.
Q:
Allen Furniture needs to produce 850 chairs, 500 tables, and 300 desks
to fill an order. It has
14,000 square feet of lumber, 2,000 hours of production time, and 6,000 pounds of screws available. It outsources part of the production to Mike's Furniture Company. The solution produced by Excel's Solver is given below. Based on the given output by Solver, which of the following statements is true?
A:
Mike's Furniture Company will manufacture 340 tables. OR
There will be a savings of 310 production hours.
Q:
Allen Furniture needs to produce 850 chairs, 500 tables, and 300 desks to fill an order. It has
14,000 square feet of lumber, 2,000 hours of production time, and 5,000 pounds of screws available. It outsources part of the production to Mike's Furniture Company. The solution produced by Excel's Solver is given below. Based on the given output by Solver, which of the following statements is true?
A:
Mike's Furniture Company charges Allen Furniture $165 for each desk. OR
The maximum revenue with outsourcing is $170,500. OR
Mike's Furniture Company charges Allen Furniture $95 for each chair.
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200
hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
What are the decision-making variables?
A:
Number of chairs, tables, and desks
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
Which resource did Mike run out first after running the problem through Excel’s Solver?
A:
None
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
Which resource(s) did Allen run out first after running the problem through Excel’s Solver?
A:
Screw
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Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
How many chairs, tables, and desks were delivered after running the problem through Excel’s Solver?
A:
800, 800, and 460, respectively
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
How many chairs, tables, and desks did Allen deliver after running the problem through Excel’s Solver?
A:
800, 300, and 0, respectively
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
How many chairs, tables, and desks is Allen supposed to deliver?
A:
800, 800, and 460, respectively
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
How many chairs, tables, and desks did Allen make after running the problem through Excel’s Solver?
A:
0, 500, and 460, respectively
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
How much labor time has left for Allen after delivering the order?
A:
400 hours
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
How much lumber has left for Allen after delivering the order?
A:
1,900 square feet
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $160 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
What is the value of the objective function after running the problem through Excel’s Solver?
A:
$170,700
Q:
Allen is in a business of making chairs, tables, and desks. He sells each chair for $140, table for $145, and desk for $120. Each chair, table, and desk consumes 10, 12 and 15 square feet of lumber; 1.5, 2, and 2.5 hours of labor; and finally 4, 6, and 7 pounds of screws, respectively. He needs to deliver at most 800 chairs, at most 800 tables, and at least 460 desks. He has a total of 13,500 square feet of lumber, 2,200 hours of labor, and 5,000 pounds of screws. He asks another furniture maker Mike to help him produce and deliver some of his order. Mike has unlimited surplus resources that can deliver any and all parts of Allen’s order. Mike charges Allen $100, $110, and $125 for each chair, table, and desk. Allen delivers all the chairs, tables, and desks to their limits.
What is the objective function?
A:
Q:
The Acme Company needs to fill an order for 120 gizmos and 150 gadgets. Each gizmo requires 3.5 production hours and each gadget requires 4 hours of production. If the Acme Company has 1,000 production hours available,_______________.
A:
they will be short by 20 hours
Q:
The Acme Company manufactures tables and chairs. Each table sells for $300, and each chair sells for $125. Acme is considering outsourcing the making of some tables and chairs to
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Company X. If Acme decide to outsource, the revenue on each table made by Company X will be $100, and on each chair made by Company X, it will be $50. Which of the following is true?
A:
It is possible for overall revenue to increase with outsourcing. OR
Company X charges the Acme Company $200 for each table that it makes.
Q:
The Acme Company needs to fill an order for 150 gizmos and 200 gadgets. Each gizmo requires 3 hours of production time and 2 pounds of hardware. Each gadget requires 2.5 hours of production time and 2.5 pounds of hardware. The Acme Company has a maximum of 800 hours of production time and 700 pounds of hardware available. If the Acme Company does not outsource part of the order, which of the following will happen?
A:
It will not have the resources to fill the order. OR It will be 100 pounds short on hardware.
Q:
Which of the following is a reason that a company might want to outsource all or part of the making of a product or products?
A:
Improving in-house efficiency OR
The ability to fulfill large orders
Q:
Company A produces gizmos and gadgets. A linear programming model yields an optimal solution that meets the boundaries of the constraints. The optimal solution results in the production of 200 gizmos and 150 gadgets, which produce a revenue of $41,500. An alternate model that involved outsourcing the production of some of the gizmos and gadgets to Company B was produced. An alternate optimal solution resulted in Company A producing 175 Gizmos and 120 Gadgets and Company B producing 75 gizmos and 60 gadgets. The overall revenue for
Company A with the alternate optimal solution is $43,250. Which of the following is true?
A:
The overall revenue increased with the alternate solution. OR
The alternate solution resulted in the production of 50 more gizmos.
Q:
There are many reasons that a company may decide to outsource.
_______________
is not a reason to outsource.
A: The opportunity to share revenue with another company
Q:
Joe's Electronics makes remote-controlled cars and boats. Each car made by Joe's Electronics sells for $75, and each boat sells for $90. Joe is considering outsourcing the production of some cars and boats to Jill's Electronics. Jill will charge Joe $50 for each car and $60 for each boat. If C represents the number of cars, B represents the number of boats made by Joe, X represents the number of cars, and Y represents the number of boats made by Jill, which of the following is true?
A:
If Joe outsources, the revenue made by Jill on each boat will be $30. OR
If Joe outsources, the objective function for revenue will be 75C + 90B + 25X + 30Y.
Q:
Joe's Electronics produces headphones and speakers. Each set of headphones sells for $50, and each set of speakers sells for $60. Joe is considering outsourcing the production of some headphones and speakers to Bobbie's Tech Company. Bobbie will charge Joe $38 for each set of headphones and $45 for each set of speakers. Let HJ represent the number of headphones and SJ the number of speakers produced by Joe. Let HB represent the number of headphones and SB the number of speakers produced by Bobbie. Which of the following is true?
A:
Joe will keep $15 of revenue for each set of speakers produced by Bobbie. OR
The objective function to maximize revenue without outsourcing
is 50HJ + 60SJ.
Q:
Joe's Electronics makes remote-controlled cars and boats. Each car made by Joe's Electronics sells for $75, and each boat sells for $85. Joe has a total of 200 production hours available and $2,000 of capital available to produce the cars and boats. Joe is considering outsourcing the production of some cars and boats to Jill's Electronics. Jill will charge Joe $50 for each car and $55 for each boat. Based on the given Solver output, which of the following statements is correct?
A:
Joe will make all of the remote-controlled cars. OR There will be a surplus of available capital.
Q:
A:
Q:
A:
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