A manufacturer of face masks mass produces them at 4 of its plants for its 5 different retail customers. Unfortunately, it is not able to produce enough face masks to meet the demands of all its customers and it is now considering no longer producing these face masks for all 5 of these customers. Currently, the following table contains most of the information necessary to make manufacturing decisions for the upcoming planning period (3 months).

Profits/1000 masks ($):

Plant retail customer

A B C D E capacities (1000s)

1 675 600 725 585 810 50

2 725 725 785 730 640 70

3 850 620 740 655 730 95

4 700 600 720 620 795 45

Demands (1000s) 80 70 100 90 60

Additional information:

• it costs $1000 per planning period for keeping customers B, D and E as customers and $3000 per period for keeping customers A and C
• a customer must be guaranteed at least 3000 masks if it is not dropped from the manufacturer

Using x_ijs (in 1000s) as the amounts shipped from plant i (row i) to customer j (column j), and A, B, C, D and E as the variables to determine whether or not to keep customers A, B, , formulate the following in order to maximize total profits.

1. The objective function (you can use after the first 2 x_ijs and before the last 2 x_ijs) if customers may be dropped by the manufacturer

2. The basic (i.e., shipping) constraint for plant 4

3. The basic (i.e., demand) constraint for customer A assuming all customers will continue receiving shipments

4. The demand constraint for customer C assuming that customers may be dropped

5. The constraint that at least 6 (1000s) must be shipped from plant 4 to retail customer E

6. The amount shipped from plant 4 to customer C must be within 2 (1000s) of the amount shipped from plant 4 to customer B

7. At least twice as many units must be shipped from plant 3 to customer D as is shipped from plant 4 to customer D