- #1
fishturtle1
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Homework Statement
A company has three machines to make units of A. Input and output data for 1 hr of operation of each machine are as follows:
Input / Input / Output
Raw Material (lb) / Labor(worker-hrs) / units of A
Machine 1: 80 / 16 / 37
Machine 2: 50 / 35 / 43
Machine 3: 76 / 33 / 52
The company must produce 2000 units of A weekly. The company can purchase up to 1 ton of the raw material for $4/lb from one source and an unlimited amount from another source for $5.50 / lb. The firm was 900 hr of labor available at $8/hr, and an additional 200 hr of overtime available at $12/hr. The company pays only for the labor and raw material it uses. How many hours could each machine be used to meet demands at minimum cost?
Set up the problem but do not solve.
Homework Equations
The Attempt at a Solution
Let Machine 1 = X, Machine 2 = Y, and Machine 3 = Z
So to deal with raw materials: ##80X + 50Y + 76Z - t \le 2,000##
where t is the amount bought for $5.50/lb.
To deal with the labor hours: ##16X + 35Y + 33Z + s \le 1100##
and ##s \le 200##
and ##16X + 35Y + 33Z \le 900##
we also need 2000 units of A: ##37X + 43Y + 52Z = 2000##
minimize: ##4(80X + 50Y + 76Z) + 5.50t + 8(16X + 35Y + 33Z) + 12s##
i'm not really sure I did the raw materials right.. Is it enough to say "where t is the amount bought for $5.50" ?