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.

Answer 1

Answer:

Step-by-step explanation:

Let $x_m$ and $x_w$ be the production level of milk and white chocolate-covered strawberries respectively. According to the given data, we know the total profit will be

$P(x_m,x_w)= 2.25x_m+ 2.50x_w$

The restrictions can be written as

$x_m+x_w \leq 800$

$x_w\leq x_m/2$

$x_w\leq 200$

All the restrictions can be plotted in the same graph to find the feasible region where all of them are met. The graph is shown in the image below

The optimal solution will be the level of production such that

* All restrictions are met

* The total profit is maximum

The optimal level of production can be found in (at least) one of the vertices of the feasible region. We'll try each one as follows

P(0,0)=0

P(400,200)=$2.25 (400)+$2.50 (200) = $1400

P(600,200)=$2.25 (600)+$2.50 (200) = $1850

P(800,0)=$2.25 (800)+$2.50 (0) = $1800

We must produce 600 milk chocolate-covered strawberries and 200 white chocolate-covered strawberries to have a maximum profit of $1850/month