1. A firm operates two distribution centers, one in Phoenix and the other is Chi

Question

1. A firm operates two distribution centers, one in Phoenix and the other is Chicago. A customer in College Station, TX needs solar panels produced by the firm. The cost to produce a solar panel in Phoenix is $349, and shipment to College Station is $63. The cost to produce a solar panel in Chicago is $349, and shipment to College Station is $47. Phoenix can supply at most 13 panels, and Chicago up to 29. The customer wants 21 panels. Structure this as an optimization model?

2. How does the problem in #1 change if the cost to produce a panel in each city changes? Specifically, the cost to produce a solar panel in Phoenix is $349 and the cost to produce a solar panel in Chicago is $379. Structure this optimization model.

Explanation / Answer

Let a,b be the number of panels produced in Phoenix and Chicago.

Then a+b=21

Total Cost=a(349+63)+b(349+47)=412a+396b

Clearly cost of production in Chicago is less than that of Phoenix.

a<=13 and b<=21

Hence we need to minimise cost.

Clearly as Chicago cost of production is less and the requirement is less than the maximum capacity.

Total panels will be manufactured at Chicago and Hence Total Cost=8316, a=0,b=21

b)Now Cost=412a+426b

Here the case changes but as the cost of production in Phoenix is lower,we first fill the orders in Pheonix,next we come to Chicago

Hence a=13,b=21-13=8, Cost=412*13+426*8=8764

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.