The deckers clothing company produces men’s pajamas and ladies’ nightgowns. pajamas are made in sets of shirts and pants while nightgowns are one-piece. each pajama shirt requires 2 yards of cloth and each pair of pajama pants requires 3 yards of cloth, while each nightgown requires 4 ½ yards of cloth. during the next three months the following demands for pajama shirt and pants pairs must be met on time: month 1, 140,000 sets; month 2, 155,000 sets; month 3, 170,000. for nightgowns the monthly demands are 100,000, 140,000, and 120,000, respectively. in each month 1.3 million yards of cloth are available for purchase. of course, deckers can elect to purchase less than these amounts. in each month it costs $8 to make a set of pajamas on regular time and $11 to make a set on overtime. for nightgowns the regular and overtime costs are $6 and $9. additionally, in each month the total number of nightgowns and pajama sets together can be no more than 150,000 produced on regular time, but an unlimited number can be produced on overtime. at the end of each month a holding cost of $1 per product set is assessed. formulate and solve the mathematical programming model to determine how to meet demand for pajamas at the minimum possible cost. assume there are 15,000 sets of pajamas and 9,000 nightgowns available in inventory at the beginning of month 1.