The small Adele19 textile company knits products p = 1,

c, 79 on a variety of machines m = 1,

c, 48 to meet known output quotas qp pounds for the next week. The variable cost per pound of making product p on machine m is known cm, p. Machines operate with changeable cylinder types j = 1,

c, 14, which have different combinations of knitting needles, and thus yield different quantities am,j,p (pounds) of product p per hour on machine m. A total of 100 hours is available on each machine over the next week, but a setup time sm,j must be deducted for each cylinder type j used on each machine m. Adele wants to find a minimum total variable cost schedule that conforms to all constraints. Formulate an ILP model of this production scheduling problem using decision variables (m = 1,

c, 48;

j = 1,

c, 14; p = 1,

c, 79)

xm,j,p ! pounds of product p made on machine m with cylinder type j ym,j ! c 1 if cylinder type j is used on machine m 0 otherwise