A chocolate factory has two products, white and dark chocolate. How much of each

ID: 3836707 • Letter: A

Question

A chocolate factory has two products, white and dark chocolate. How much of each should it produce to maximize the profit?

Assume it makes x1 boxes of white and x2 boxes of dark per day, with a profit of $1 on a white box, and a profit of $6 on the dark box.

The daily demand for these chocolates is limited to at most 200 boxes of white and 300 boxes of dark.

Finally, the current work force can produce at most 400 boxes of chocolate per day.

Your job is to present this profit optimization as a Linear Program in standard form.

Then present it in slack form too.

You are not required to solve the problem, but if you provide the correct answer you get 3 bonus point.

We want to formulate an LP that describes the production plans that the firm

can use to maximize its profits.

The relevant variables are the number of finished and unfinished dark,I

will call them TF and TU , and the number of finished and unfinished chairs, CF

and CU . The revenue is (using the table):

70TU + 140TF + 60CU + 110CF ,

, while the cost is 40TU + 40TF + 30CU + 30CF (because lumber costs $1 per

board foot).

The constraints are:

1. 40TU + 40TF + 30CU + 30CF 40000.

2. 2TU + 5TF + 2CU + 4CF 6000.

The first constraint says that the amount of lumber used is no more than what

is available. The second constraint states that the amount of labor used is no

more than what is available.

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