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European University of Business
Europejska Wyzsza Szkola Biznesu
M.B.A Program
Learning Center at “Berlin”
Academic Year: 2019/2020
A Silicon Valley firm specializes in making four types of silicon chips for personal computers. Each chip must go through four stages of processing before completion. First the basic silicon wafers are manufactured, second the wafers are laser etched with a micro circuit, next the circuit is laminated onto the chip, and finally the chip is tested and packaged for shipping. The production manager desires to maximize production during the next month. During the next 30 days, she has enough raw material to produce 4000 silicon wafers. Moreover, she has 600 hours of
etching time, 900 hours of lamination time, and 700 hours of testing time. Taking into account depreciated capital investment, maintenance costs, and the cost of labor, and that chip types are produced by batches of 100s, each raw silicon wafer is worth $1, each hour of etching time costs $40, each hour of lamination time costs $60, and each hour of inspection time costs $10.
If we represent by X1, X2, X3, and X4 the number of 100 chip batch types, and we are provided with the following table giving for each chip type the number of units of resources needed to manufacture of batch types
Type 1(100s) Type 2(100s) Type 3(100s) Type 3(100s) Available
Raw wafers 100 100 100 100 4000
Etching 10 10 20 20 600
Lamination 20 20 30 20 900
Testing 20 10 30 30 700
Price per chip ( not per 100 batch) $61 $58 $80 $64
Questions
1. Formulate the problem as a linear program with a profit maximization as an objective.
2. How many chip batches types the company should produce to maximise the total profit contribution?
3. Are there any constraints which are binding?
4. Interpret the slack and /or surplus in each constraint.
5. Find the ranges in which the profit contributions can change without affecting the current production plan.
6. If there is a sudden additional demand for our chips of type 2 , we may need either to hire another employee or to use our current employees overtime at the lamination department. Employees at the lamination department are ready to work overtime for $1,4 per hour. Would you accept their request or refuse it. Justify your answer.
7. The President of the company SLICON VALLEY is wondering whether it is possible to have more flexibility in production to respond better to the market and shortage of resources. Could you propose for him alternative production plans?
8. If the profit contribution of chip type 2 is increased by $ 1. What will be the impact on our current plan?
9. If the amount of time available at the Lamination department is decreased by 40 hours because of the absence of one of the employees and in the meantime the amount of time at the inspection department is increased by 50 hours, what will be the impact on our current optimal plan?
10. The Marketing manager is an executive M.B.A. student at our Campus in Warsaw is totally convinced that producing a new type of chip (type 5), will increase tremendously the total profit of the company. If the production of one batch of type 5 chip (100) requires 80units of Raw Wafers department, 20 hours at the Etching department, 10 hours at the lamination department, and 10 hours at the inspection department its individual profit contribution is $70, would you support his suggestion? Explain.
Combined Report for SILICON VALLEY A

Decision Solution Unit Cost or Total Reduced Basis Allowable Allowable
Variable Value Profit c(j) Contribution Cost Status Min. c(j) Max. c(j)
1 X1 0 61,0000 0 0 at bound -M 61,0000
2 X2 25,0000 58,0000 1 450,0000 0 basic 58,0000 64,0000
3 X3 10,0000 80,0000 800,0000 0 basic 64,0000 91,5000
4 X4 5,0000 64,0000 320,0000 0 basic 64,0000 80,0000
Objective Function (Max.) = 2 570,0000
Left Hand Right Hand Slack Shadow Allowable Allowable
Constraint Side Direction Side or Surplus Price Min. RHS Max. RHS
1 C1 4 000,0000 = 4 000,0000 0 0,2300 3 666,6670 4 500,0000
2 C2 550,0000 = 600,0000 50,0000 0 550,0000 M
3 C3 900,0000 = 900,0000 0 1,6000 800,0000 950,0000
4 C4 700,0000 = 700,0000 0 0,3000 600,0000 800,0000

Combined Report for SILICON VALLEY B

Decision Solution Unit Cost or Total Reduced Basis Allowable Allowable
Variable Value Profit c(j) Contribution Cost Status Min. c(j) Max. c(j)

1 X1 10,0000 61,0000 610,0000 0 basic 61,0000 69,0000
2 X2 20,0000 58,0000 1 160,000 0 basic 42,0000 58,0000
3 X3 10,0000 80,0000 800,0000 0 basic 64,0000 91,5000
4 X4 0 64,0000 0 0 at bound -M 64,0000

Objective Function (Max.) = 2 570,0000
Left Hand Right Hand Slack Shadow Allowable Allowable
Constraint Side Direction Side or Surplus Price Min. RHS Max. RHS
1 C1 4 000,0000 = 4 000,0000 0 0,2300 3 666,6670 4 500,0000
2 C2 500,0000 = 600,0000 100,0000 0 500,0000 M
3 C3 900,0000 = 900,0000 0 1,6000 800,0000 950,0000
4 C4 700,0000 = 700,0000 0 0,3000 600,0000 900,0000

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