Question: A tailor makes wood tweed sport coats and wool slacks. He is able to get a shipment of 150 square yards of wool cloth from Scotland each month to make coats and slacks, and he has 200 hours of his own labor to make them each month. A coat requires 3 square yards of wool and 10 hours to make, and a pair of slacks requires 5 squares yards of wool and 4 hours to make. The tailor earns a $50 in profit from each coat he makes and $40 from each pair of slacks. He wants to know how many coats and pair of slacks to produce to maximize profits.

(a). Formulate an integer linear programming model for this problem.

(b).Determine the integer solution to this problem by using the computer. Compare this solution to the solution without integer restrictions and indicate whether the rounded-down solution would have been optimal.