A clothier makes coats and slacks. The two resources required are wool cloth and labor. The clothier has 150 square vard

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A clothier makes coats and slacks. The two resources required
are wool cloth and labor. The clothier has 150 square vards of wool
and 200 hours of labor available. Each coat requires 3 square yards
of wool and 10 hours of labor, whereas each pair of slacks requires
5 square yards of wool and 4 hours of labor. The profit for a coat
is $50, and the profit for slacks is $40. The clothier wants to
determine the number of coats and pairs of slacks to make so that
profit will be maximized.
a. Formulate a linear programming model for this
problem.
b. Solve this model by using graphical analysis, then
explicitly find the optimal solution and optimal objective function
value.
c. Find the value of the slack or surplus associated
with each constraint.