Q1 Linear Programming -- Product Output 

A company produces 3 different products, A, B, and C.  All products require time in up to 5 different processing departments.  The amount of time each product requires with each department is listed in the table below:

             Product A Product B    Product C   Available

Melting    6 hrs        2 hr         0 hrs         1200 hrs

Cooling    3 hrs        2 hrs       1 hr         1240 hrs

Shaping   3 hrs         2 hrs      1 hr            2000 hrs

Sanding   2 hrs         3 hr       3 hrs           1875 hrs

Painting   1 hr           2 hrs      2 hrs          1550 hrs

Suppose product A sells for $200/unit, product B sells for $225/unit, and product C sells for $125/unit.  And suppose that all products have a guaranteed buyer (i.e., no matter how many are produced it will be sold for the asking price).  Management has asked for your recommendations about how many of each product type to produce that maximize revenue.  So question…

Question:

a) How much of each product do you recommend be produced that you believe maximizes revenue?  

b) How much revenue would be made if they followed your recommendation?