Radford+Castings (2) - Radford Castings can produce brake shoes on six different machines The following table summarizes the manufacturing costs

Radford+Castings (2) - Radford Castings can produce brake...

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Radford Castings can produce brake shoes on six different machines. The following table summarizes the manufacturing costs associated with producing the brake shoes on each machine along with the available capacity on each machine. If the company has received an order for 1,800 brake shoes, how should it schedule these machines? Machine Fixed Cost Variable Cost Capacity 1 $1000 $21 500 2 $950 $23 600 3 $875 $25 750 4 $850 $24 400 5 $800 $20 600 6 $700 $26 800 a. Formulate a Linear Program to solve this production problem d is binary number X 1 , x 2 , x 3, x 4 , x 5 , and x 6 - unknown quantities to manufacture on each Machine d 1 , d 2 , d 3 , d 4 , d 5 , d 6 - 1 if Machine 1 (2, 3, 4, 5, and 6) is used, 0 otherwise Objective Function Z = min total cost min z = 1000d 1 + 950d 2 + 875d 3 + 850d 4 + 800d 5 + 700d 6 + 21x 1 + 23x 2 + 25x 3 + 24x 1 + 20x 2 + 26x 3 st. X 1 + x 2 + x3 + x4 + x 5 + x 6 >= 1800 (production requirement) X 1 <= 500d 1 (Machine 1 capacity is available only if it is being used) X 2 <= 600d 2 (Machine 2 capacity is available only if it is being used) X 3 <= 750d 3 (Machine 3 capacity is available only if it is being used) X 4
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