1. Acme manufacturing company decides to produce two groups of products: group A
ID: 3105832 • Letter: 1
Question
1. Acme manufacturing company decides to produce two groups of products: group A and group B. Each group-A product will bring in $3 profit and each group –B product will bring in $4 profit. It takes 5 minutes to make a group-A product on machine I and 3 minutes on machine II. The group-B product need 3 minutes on machine I and 4 minutes on machine II. There are 6 hours available on machine I and 8 hours available on machine II. How many products of each group should Acme make in order to maximize its profit?
Explanation / Answer
let the number of units of A made be x1 ;
no of units of B made be x2
maximize z = 3 x1 + 4 x2 ;
subject to ,
5 x1 + 3 x2 < = 6 * 60
3 x1 + 4 x2 < = 8 * 60
OR
maximize z = 3 x1 + 4 x2 ;
subject to ,
5 x1 + 3 x2 < = 360
3 x1 + 4 x2 < = 480
solving the above inequality ,
x1 = 0 , <-------------units of A
x2 = 120 units ; <---------units of B
profit z = $ 480 <--------------ans
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