Question

An apple pie uses 4 cups of apples and 3 cups of flour. An apple cobbler uses 2 cups of apples and 3 cups of flour. You have 16 cups of apples and 15 cups of flour. When you sell these at the farmers market you make $3.00 profit per apple pie and $2.00 profit per apple cobbler. Use linear programming to determine how many apple pies and how many apple cobblers you should make to maximize your profit.

1. let ×= the number of apple pies you make and y= the number of apple cobblers you make. Write an inequality to show the constraint on the amount of apples you have?
2. Write an inequality to show the constraint on the amount of flour you have .
3. Write any non negativity contraints on x and y

Answer 1

Part 1:

Given that x represents the number of apple pies that can be made and y represents the number of apple cobblers that can be made.

Given that an apple pie uses 4 cups of apples and an apple cobbler uses 2 cups of apples and there are 16 cups of apples available.

An inequality to show the constraint on the amount of apples available is given by:

4x + 2y ≤ 16



Part 2:

Given that an apple pie uses 3 cups of flour and an apple cobbler uses 3 cups of flour and there are 15 cups of flour available.

An inequality to show the constraint on the amount of flour available is given by:

3x + 3y ≤ 15



Part C:

The non negativity contraints on x and y are:

x ≥ 0 and y ≥ 0