Question

The New England Cheese Company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 12-ounce containers, which are then sold to distributors throughout the Northeast. The Regular blend contains 80% mild cheddar and 20% extra sharp, and the Zesty blend contains 60% mild cheddar and 40% extra sharp. This year, a local dairy cooperative offered to provide up to 7,995 pounds of mild cheddar cheese for $1.20 per pound and up to 3,030 pounds of extra sharp cheddar cheese for $1.40 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.20 per container. If each container of Regular is sold for $1.85 and each container of Zesty is sold for $2.20, how many containers of Regular and Zesty should New England Cheese produce?

Answer 1

	Regular	Zesty	Cost
Mild	0.8	0.6	$1.20
Extra Sharp	0.2	0.4	$1.40
Price of container	$1.85	$2.20
Cost for Blend and package =	$0.20

Data in pounds, 12 ounces = 0.75 pounds
	Regular	Zesty
Mild	0.8*0.75 = 0.6	0.6*0.75 = 0.45
Extra Sharp	0.2*0.75 = 0.15	0.4*0.75 = 0.3

Cost of Regular Cheese = (0.6*1.2) + (0.15*1.4) + 0.2 = 1.13

Cost of Zesty Cheese = (0.45*1.2) + (0.3*1.4) + 0.2 = 1.16   

Profit for regular Cheese = 1.85 - 1.13 = 0.72

Profit for Zesty Cheese = 2.2 - 1.16 = 1.04

Objective Function:

z = 0.72*R + 1.04*Z

Optimal solution:

R =	9200
Z =	5500
Profit =	$12,344.00