A semiconductor fabrication plant produces two graphic chipsets (4091Tii and 7951XTT) that require both silicon wafer...

 

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A semiconductor fabrication plant produces two graphic chipsets (4091Tii and 7951XTT) that require both silicon wafer and precious metal. The owner wants to determine how many units of each product are to be produced so as to maximize the profit. For each unit of 4091Tii, 60mm² of silicon wafer and 20g of precious metal are required. For each unit of 7951XTT, 20mm² of silicon wafer and 40g of precious metal are required. The company has 15,000mm² of silicon wafer and 12,000g of precious metal. Each 4091Tii, gives a profit of $600, and each unit of 7951XTT gives a profit of $400. Any excess over 170 units of 4091Tii will impose a negative impact on the marketing strategy of the company, so such excess has been ruled out. Similarly, any excess over 240 units of 7951XTT will impose a similar effect which has been ruled out as well. (a) Formulate the above problem as a Linear Programming (LP) problem. [2 points] Hint: Denote X₁ as the the number of 4091Tii to be produced and X₂ as the number of 7951XTT to be produced. (b) Solve this LP problem graphically. What is the maximum total profit? [2 points] A semiconductor fabrication plant produces two graphic chipsets (4091Tii and 7951XTT) that require both silicon wafer and precious metal. The owner wants to determine how many units of each product are to be produced so as to maximize the profit. For each unit of 4091Tii, 60mm² of silicon wafer and 20g of precious metal are required. For each unit of 7951XTT, 20mm² of silicon wafer and 40g of precious metal are required. The company has 15,000mm² of silicon wafer and 12,000g of precious metal. Each 4091Tii, gives a profit of $600, and each unit of 7951XTT gives a profit of $400. Any excess over 170 units of 4091Tii will impose a negative impact on the marketing strategy of the company, so such excess has been ruled out. Similarly, any excess over 240 units of 7951XTT will impose a similar effect which has been ruled out as well. (a) Formulate the above problem as a Linear Programming (LP) problem. [2 points] Hint: Denote X₁ as the the number of 4091Tii to be produced and X₂ as the number of 7951XTT to be produced. (b) Solve this LP problem graphically. What is the maximum total profit? [2 points]

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