Posted on by Judy

Acme Products produces two products: C and D. Product C sells for $11/unit and D sells for $23/unit. A unit of C requires 2 hours on machine 1 and 1 unit of material E. A unit of D requires 2 hours on machine 2, 2 units of material E, and 1 unit of C. There are 1,300 hours available on machine 1, and 500 hours on machine 2. A unit of material E may be bought for $5, or produced (at no cost) using 2 hours on machine 1. Formulate an LP to maximize profits. 1. There should be 4 variables, one for product C, One for product D, one for E to be bought and one for E to be produced 2. The Price for D should be 23-11 =12 since D is using C for production

Let,
X1 = No. of product C to be produced
X2 = No. of product D to be produced
X3 = No. of product E to be bought
X4 = No. of product E to be produced
Objective Function: Maximize. Z = Total Profit = Revenue – Cost = 11(X1 – X2) + 23X2 – 5X3
or, Z = 11X1 + 12X2 – 5X3
Subject to,
2X1 + 2X4 ≤ 1300 (Machine 1 available time)
2X2 ≤ 500 (Machine 2 available time)
1X1 + 2X2 – X3 – X4 = 0 (Balance of E)
X1, X2, X3, X4 ≥ 0
———————–
LINDO Code
Max 11X1 + 12X2 – 5X3
ST
2X1 + 2X4
 
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