Question

For the following problem state the objective function and the constraints. DO NOT solve:

A local group is planning to raise as much money as they can by making and selling umbrellas. They intend to make two models: the Sprinkle and the Hurricane.
The amount of cloth, metal, and wood used in making each model, the amount of each material available on a given day and the profit for each model are:

Sprinkle Hurricane Total Available
Cloth (sq yd) 1 2 500
Metal (lbs) 2 3 600
Wood (lbs) 4 7 800
Profit ($) 3 5

Answer 1

If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit P can be expressed as:

`P=3S+5H`

The restriction for cloth can be written as:

`S+2H\leq500`

The restriction for metal can be written as:

`2S+3H\leq600`

The restriction for wood can be written as:

`4S+7H\leq800`

The condition for S and H to be positive is:

`S, H \geq0`

Explanation:

We have an objective function that, in this case, we want ot maximize.

This function is the Profit (P).

If we define S as the number Sprinkle's umbrellas, and H as the Hurricane's umbrellas, the profit can be expressed as:

`P=3S+5H`

We have 3 restrictions, plus the condition that both S and H are positive.

The restriction for cloth can be written as:

`S+2H\leq500`

The restriction for metal can be written as:

`2S+3H\leq600`

The restriction for wood can be written as:

`4S+7H\leq800`

The condition for S and H to be positive is:

`S, H \geq0`