Question

The Marketing Club at your college has decided to raise funds by selling three types of T-shirt: one with a single-color "ordinary" design, one with a two-color "fancy" design, and one with a three-color "very fancy" design. The club feels that it can sell up to 300 T-shirts. "Ordinary" T-shirts will cost the club $6 each, "fancy" T-shirts $8 each, and "very fancy" T-shirts $10 each, and the club has a total purchasing budget of $3,200. It will sell "ordinary" T-shirts at a profit of $3 each, "fancy" T-shirts at a profit of $6 each, and "very fancy" T-shirts at a profit of $3 each.

How many of each kind of T-shirt should the club order to maximize profit? HINT [See Example 3.]

Answer 1

Fancy 300 T-shirt

Ordinary 133 T-shirt

Step-by-step explanation:

Cost per T-shirt

Ordinary $ 6

Fancy $ 8

Very Fancy $ 10

Budget constraing $ 3,200

We have to calculatethe contribution per dollar as we have a constrain on that:

`\left[\begin{array}{cccc}&$Ordinary&$Fancy&$Very Fancy&\\$Profit&9&14&13&\\$Cost&6&8&10&\\$CM&3&6&3&\\$Constrain resource&6&8&9&\\$CM per constrain&0.5&0.75&0.33&\\\end{array}\right]`

First we purchase Fancy:

300 x 8 = 2,400

Then, the 800 dollar left will be for Ordinary:

800 / 6 = 133 units