A company manufactures a product at its plants in Q,R, and S: Then ships the product to its customers in C,D, E and F. The profits (in dollars per unit) are as follows:

from Q to C, D, E, and F: 20, 17, 16, and 19.

from R to C, D, E, and F: 17, 18, 20, and 16.

from S to C, D, E, and F: 18, 20, 18, and 17.

The monthly demand from C, D, E, and F are: 4400, 7000, 3500, and 4000 units respectively.

On the other hand, the monthly capacity at plants Q, R, and S are: 7000, 6000, and 9000 units.

Develop a linear programming model that can be used to determine the distribution plan that will maximize total monthly profit. Check if customers will experience a shortage and if plants will have unused supply capacity.

The Optimal solution suggests:

The total monthly profit is ___

Plant Q send a total of __ units.

Plant R send a total of __ units.

Plant S send a total of __ units.

Plant Q will have a leftover (unused) capacity of ___ units.

Plant R will have a leftover (unused) capacity of ___ units.

Plant S will have a leftover (unused) capacity of ___ units.

Customer C will experience a shortage of ___ units.

Customer D will experience a shortage of ___ units.

Customer E will experience a shortage of ___ units.

Customer F will experience a shortage of ___ units.