MATH SOLVE

5 months ago

Q:
# Working on homework. Need help with one part of the worksheet. This is the main problem.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. Attached first is what I have so far. Attached second is what I need help with. How to I write an obgective function that I can use to evaluate the profit?

Accepted Solution

A:

let x = number of
apple pies you would make
let y= the number of apple cobblers you make
4 cups of apples
for a pie 2 cups for cobbler with 16 cups

so we have: 4x+2y<=16

3 cups of flour for both pies and cobbler we get: 3x+3y<=15.

solve the system of inequalities to get (3,2) check: 4(3) +2(2) = 12+4 = 14, this is less than 16 so this is true 3(3) + 3(2) = 9 +6 = 15 does equal 15 so this is true Now profit equation is 3x +2y = profit 3(3) +2(2) = 9+4 = 13 You can make 3 apple pies and 2 apple cobblers for maximum profit

so we have: 4x+2y<=16

3 cups of flour for both pies and cobbler we get: 3x+3y<=15.

solve the system of inequalities to get (3,2) check: 4(3) +2(2) = 12+4 = 14, this is less than 16 so this is true 3(3) + 3(2) = 9 +6 = 15 does equal 15 so this is true Now profit equation is 3x +2y = profit 3(3) +2(2) = 9+4 = 13 You can make 3 apple pies and 2 apple cobblers for maximum profit