FINALS EXAM

Question

Curtis-Roe Aviation Industries has two plants, I and II that produce the Zephyr jet engine used in their light commercial planes. The maximum capacity at Plant I is 100 units and at Plant II is 110 units per month. The engines are shipped to assembly locations in Granite City and East St. Louis. It costs $100 to ship an engine from Plant I to Granite City and $60 to ship from Plant I to East St. Louis. From Plant II, it cost $120 to ship an engine to Granite City and $70 to East St. Louis. For a certain month Granite City needs 80 engines and East St. Louis needs 70 engines. How many engines should be shipped from each Plant to each assembly location if the shipping costs are to be kept at a minimum?

Answer 1

Here's one way to think through the problem:

 

 

A total of 150 units need to be shipped during the month.

 

Units from Plant I cost either $100 (Granite City) or $60 (East St. Louis) while units from Plant II cost either $120 (Granite City) or $70 (East St. Louis). Clearly, the company ought to ship as many units from Plant I as possible. Since Plant I's maximum capacity is 100 units, that means the company should ship 100 units from Plant I and the other 50 units from Plant II.

 

Every unit shipped from Plant II will cost either $20 or $10 extra, depending on which city it's shipped to. So, the company should ship all 50 units from Plant II to East St. Louis, which only costs $10 extra per unit.

 

That means in order to minimize shipping costs, the company should ship:

 

80 units from Plant I to Granite City

20 units from Plant I to East St. Louis

0 units from Plant II to Granite City

50 units from Plant II to East St. Louis