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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.]

Respuesta :

TomShelby

Answer:

Fancy     300 T-shirt

Ordinary 133  T-shirt

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:

[tex]\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][/tex]

First we purchase Fancy:

300 x 8 = 2,400

Then, the 800 dollar left will be for Ordinary:

800 / 6 = 133 units

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