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 an 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 profit.
Let x=The number of apple pies you make. Let y=The number of apple cobblers you make Write an inequality to show the constraint on the amount of apples you have.
1a. Apple pie uses 4 cups and 3 cups of flour.
Apple cobbler uses 2 cups of apples and 3 cups of flour
You have 16 cups of apples and 15 cups of flour
Apple pie= $3.00, $2.00 apple cobbler.
X=apple pie, Y=apple cobbler
Write an inequality to show the constraint on the amount of apples you have.
4x+2y<=16
1b. Write an inequality to show the constraint on the amount of flour you have.
3x+3y<=15
1c. Write any non-negativity constraints on x and y.
Add 4x+2y<=16 and 3x+3y<=15
7x+5y<=31
7x<=31, 5y<=31
2a. Leaving your inequality from 1a in standard form, find the x and y intercepts to graph it on the coordinate plane provided.
I need help with 2a. and 1c.
Explain it ?
To solve 2a, we need to first rewrite the inequality in standard form, which is of the form Ax + By ≤ C.
The inequality from 1a is 4x + 2y ≤ 16.
To find the x-intercept, we set y = 0 and solve for x.
4x + 2(0) = 16
4x = 16
x = 4
So the x-intercept is (4, 0).
To find the y-intercept, we set x = 0 and solve for y.
4(0) + 2y = 16
2y = 16
y = 8
So the y-intercept is (0, 8).
Now we can plot these two points on the coordinate plane and draw a line through them.
For 1c, the non-negativity constraints refer to the fact that you cannot have negative quantities of apple pies or apple cobblers.
Since we cannot have a negative number of items, we add the constraints x ≥ 0 and y ≥ 0 to represent this.
So the complete set of constraints is:
4x + 2y ≤ 16
3x + 3y ≤ 15
x ≥ 0
y ≥ 0