Working on homework. need 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 with. how to i write an obgective function that i can use to evaluate the profit?

In this exercise we have to have knowledge about finances, in order to be able to calculate and write a function that corresponds to profits, so:

Then using the information given in the text we can write that:

So writing the function we have that corresponds to:

So writing the second function that corresponds to 3 cups of flour, we have:

So solving these systems we find:

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 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

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