Manufacturing—Resource Allocation A clothing manufacturer makes denim and hooded fleece jackets. Each denim jacket requires 2 labor-hours for cutting the pieces, 2 labor-hours for sewing, and 1 labor-hour for finishing. Each hooded fleece jacket requires 1 labor-hour for cutting, 4 labor-hours for sewing, and 1 labor-hour for finishing. There are 42 labor-hours for cutting, 90 labor-hours for sewing, and 27 labor-hours for finishing available each day. The profit is $9 per denim jacket and $5 per hooded fleece jacket.
(a) Fill in the following chart:
Denim
Hooded fleece
Available hours
Cutting
Sewing
Finishing
Profit
(b) Let x be the number of denim jackets made each day. Let y be the number of hooded fleece jackets made each day. Refer to the chart, and give three inequalities that x and y must satisfy due to the available labor-hours.
(c) Give other requirements that x and y must satisfy.
(d) Find the profit in making x denim jackets and y hooded fleece jackets.
(e) Graph the feasible set for the clothing problem.
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