Daisy drugs manufactures two drugs: drug 1 and drug 2. the drugs are produced by

Question

Daisy drugs manufactures two drugs: drug 1 and drug 2. the drugs are produced by blending together two chemicals: chemical 1 and chemical 2. by weight, drug 1 must contain at least 65% chemical 1. and drug 2 must contain 55% chemical 1. drug 1 sells for $6/oz and drug 2 sells for $4/oz. chemicals 1 and 2 can be produced by one of two production processes. running process 1 for an hour requires 3 oz raw materials and 2 hours skilled labor and yields 3 oz of each chemical. running process 2 for an hour requires 2 oz of raw materials and 3 hours skilled labor and yields 3 oz chemical 1 and 1 oz chemical 2. a total of 120 hours of skilled labor and 100 oz of raw material are available. formulate an LP that can be used to maximize the sales revenue.


i know the LP is going to be: max 6d1+4d2.
but i'm having trouble coming up with the constraints. Can someone help me out?

Explanation / Answer

Note that all defined variables are >= 0 Let c1, c2 = amount of chemical c1, c2, respectively Let p1, p2 = process time for process p1, p2, respectively Let m = material used Let l = labor used Let x and y represent the percentage of each chemical used for drug 1. Then d1 = x*c1 + y*c2 x + y = 1.00 x>=0.65 Let d2 = 0.55*c1 + 0.45*c2 -- Note that these percentages are defined. Hmmm (thought sketching here - not used in final constraints) p1 = 3m + 2L yields 3 oz of c1 & 3 oz of c2 p2 = 2m + 3L yields 3 oz of c1 & 1 oz of c2 So, 3 p1 + 2 p2

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