Bussiness Economics Problem A company makes three types of

Bussiness Economics - Problem

A company makes three types of candy and packages them in three assortments. Assortment I contains 4 sour, 4 lemon, and 12 lime candies, and sells for $9.40. Assortment II contains 12 sour, 4 lemon, and 4 lime candies, and sells for $7.60. Assortment III contains 8 sour, 8 lemon, and 8 lime candies, and sells for $11.00. Manufacturing costs per piece of candy are $0.20 for sour, $0.25 for lemon, and $0.30 for lime. They can make 4,800 sour, 3,800 lemon, and 6,000 lime candies weekly. How many boxes of each type should the company produce each week in order to maximize its profit? What is the maximum profit? The maximum profit is $ when boxes of assortment I, boxes of assortment II and boxes of assortment III are produced.

Solution

Let profit on each assortments be P1,P2 & P3

P1 = 9.4 - 5.4 = $4

P2 = $3

P3 = $5

Let a,b,c be number of boxes

Maximize Profit function (Z) = a*P1+b*P2+c*P3 = 4a+3b+5c

conditions a>=0 , b>=0 , c>=0

4a+3b>0,3b+5c>0,3b+5c>0

solve for a,b,c and get optimum fit for Z.