A company makes two types of tomato sauce, Whole (W) and Marinara (M). They created and solved a linear programming problem in order to maximize their profits in selling sauces. Whole sauce makes $1 in profit per jar, and Marinara makes $1.25 in profit per jar. There are 3 primary ingredients that make up the constraints. (1) The company has 4,480 ounces of whole tomatoes available, and a jar of W sauce uses 5 ounces and a jar of M uses 7 ounces. (2) They have 2080 ounces of basic tomato sauce, and a jar of W sauce uses 3 ounces and M uses 1 ounce. (3) They have 1,600 ounces of tomato paste, and the both the W and M sauces use 2 ounces per jar.
The optimal solution to the linear programming problem is to produce 560 ounces of Whole (W) sauce and 240 ounces of Marinara (M) sauce. The output from the program is listed below:
Objective Function Value: 860
Whole Sauce 560
Marinara Sauce 240
Constraint Slack/Surplus Dual Prices
1 0 .125
2 160 0
3 0 0.187
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
W 0.893 1.0 1.25
M 1.0 1.25 1.40
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
1 4,320 4,480 5,600
2 1,920 2,080 No Upper Limit
3 1,280 1,600 1,640
a. If the company finds a way to improve their productivity so that they can increase their profit per jar substantially, what is the maximum profit per jar they can obtain while still using this optimal solution? Give the maximum profit per jar for both types of sauce.
b)List the constraint(s) that are not binding and interpret their slack/surplus variable(s).
c)What does it mean that the right-hand side range of constraint 2 has no upper limit?