Suppose that the decision variables of a mathematical programming model are xi, j, t! amount of product i produced on manufacturing line j during week t where i = 1,c, 17; j = 1,c, 5; t = 1,c, 7.

Use summation and “for all” indexed notation to write expressions for each of the following systems of constraints in terms of these decision variables, and determine how many constraints belong to each system.

(a) Total production on any line in any week should not exceed 200.

(b) The total 7-week production of product 5 should not exceed 4000.

(c) At least 100 units of each product should be produced each week.