Question

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 5,200 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?

Answer 1

Variables

a, b, c are variables for Assortment I, II and III

objective

maximize profit

solution

		per candy			Cost				Total
candy	Optimal	Sour	lemon	Lime	Sour	lemon	Lime	revenue	Sour	lemon	Lime	cost	Revenue	profit
Assortment I	100	4	4	12	0.2	0.25	0.3	9.4	400	400	1200	540	940	400
Assortment II	0	12	4	4	0.2	0.25	0.3	7.6	0	0	0	0	0	0
Assortment III	600	8	8	8	0.2	0.25	0.3	11	4800	4800	4800	3600	6600	3000
Total									5200	5200	6000			3400
Max possible									5200	3800	6000
Constraint check									0	0	0

Maximum profit = 3400

Assortment I: 100

Assortment II: 0

Assortment III: 600