Solution:
Let the no. of gallons of milk that will be sold by itself be "x".
Let the no. of dozens of cookies that will be sold by itself be "y"
Let the gallons/dozens of packaged together milk and cookies that will be sold be "z"
Thus ,
Objective function = total profit
= 1.5x+2.5y+3z.
This has to be maximized.
Constraints:
1. x+z<=100 (as 100 gallons of milk is available per day)
2. y+z<=150 (as 150 dozen cookies is available each day)
3. x+z>=75 (stock will be at least 75 gallons of milk per day)
4. y+z = 140 (as demand for cookies is always 140 dozen per day)
5. x,y,z>=0 (non-negativity constraint)
Solving the above in solver the following solution is obtained:
X 100
Y 140
z 0
Total profit 500 Formula
1.5x+2.5y+3z
Constraints
100 <= 100 x+z<=100
140 <= 150 y+z<=150
100 >= 75 x+z>=75
140 = 140 y+z = 140
Thus maximum daily profit is $500.
This is achieved by selling 100 gallons of milk by itself and 140 dozens of cookies by itself.
