Question

Baking a tray of chocolate chip cookies takes three cups of milk and two cups of flour. Baking a tray of oatmeal raisin cookies takes one cup of milk and four cups of flour. The baker has 9 cups of milk and 16 cups of flour available. He makes $2.50 profit per tray of chocolate chip cookies and $2 profit per tray of oatmeal raisin. How many trays of each type of cookies should be make to maximize his profit?

Answer 1

Explanation:

this is a linear programming problem.

the objective is to maximize profit

let the chocolate be x

and cookies be y

Maximize

2.5x+2y=P

constraint milk

3x+y=9------------------1

constraint flour

2x+4y=16----------------2

solving 1 and 2

3x+y=9

2x+4y=16

multiply 1 by 2 and 2 3 to eliminate x we have

6x+2y=18

6x+12y=48

-0-10x=-30

10y=30

y=30/10

y=3

put y= 3 in eqn 1 we have

3x+3=9

3x=9-3

3x=6

x=6/3

x=2

two trays of chocolate

three trays of cookies

2.5x+2y=P

2.5(2)+2(3)=P

5+6=P

P=$11