Optimization equation: Your maximum profit is $____. You should produce____boxes of milk chocolate and_____boxes of white chocolate.What is the Optimization equation also?:

Question

Suppose you are starting your own company selling chocolate covered strawberries. You decide to sell the milk chocolate covered strawberries for a profit of $2.25/box and the white chocolate covered strawberries at $2.50/box. Market tests and available resources, however, have given you the following constraints. The combined production level should not exceed 800 boxes per month. The demand for the white chocolate is no more than half the demand for milk chocolate strawberries. The production level for white chocolate should be less than or equal to 200 boxes.

Using the information in the problem, write the constraints. Let x represent number of milk chocolate boxes produced, and y represent number of white chocolate boxes produced.\

Optimization equation:P=

Your maximum profit is $____.

 You should produce____boxes of milk chocolate and_____boxes of white chocolate.

Answer 1

P = 2.25x + 2.50y

0≤ y ≤ 200

0 ≤ x ≤ 800

y ≤ x/2

x+y ≤ 800

If you plot the inequalities, the intersection points of the plots are:

(0,0)

(400,200)

(600,200)

(800,0)

(0,200)

P(0,0) = 0

P(400,200) = 1400

P(600,200) = 1850

P(800,0) = 1800

P(0,200) = 500

So, the maximum profit is $1850.

Should produce 600 boxes of the milk chocolate and 200 boxes of white chocolate.