(c) A company manufactures two products: X and Y. Product X costs $8 per unit and contains 2 units of raw material 1,6 units of raw material 2 and 4 units of raw material 3. Product Y costs $10 per unit and contains 2 units of raw material 1, 2 units of raw material 2 and 12 units of raw material 3. The company has 80 units of raw mnaterial 1, 120 units of raw material 2 and 240 units of raw material 3 available. In addition, the product Y should be at least 15 units less than product X. How many units of each product should the company produce to minimize the cost of production? (1) Derive the system of equations. (ii) Use the extreme point method to solve the system. Ensure that you explain each step in the computation.
(c) A company manufactures two products: X and Y. Product X costs $8 per unit and contains 2 units of raw material 1,6 units of raw material 2 and 4 units of raw material 3. Product Y costs $10 per unit and contains 2 units of raw material 1, 2 units of raw material 2 and 12 units of raw material 3. The company has 80 units of raw mnaterial 1, 120 units of raw material 2 and 240 units of raw material 3 available. In addition, the product Y should be at least 15 units less than product X. How many units of each product should the company produce to minimize the cost of production? (1) Derive the system of equations. (ii) Use the extreme point method to solve the system. Ensure that you explain each step in the computation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(c) A company manufactures two products: X and Y. Product X costs $8 per unit and contains 2
units of raw material 1,6 units of raw material 2 and 4 units of raw material 3. Product Y
costs $10 per unit and contains 2 units of raw material 1, 2 units of raw material 2 and 12
units of raw material 3. The company has 80 units of raw material 1, 120 units of raw
material 2 and 240 units of raw material 3 available. In addition, the product Y should be at
least 15 units less than product X. How many units of each product should the company
produce to minimize the cost of production?
(1)
Derive the system of equations.
(ii)
Use the extreme point method to solve the system. Ensure that you explain each
step in the computation.
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