Math Sux (corrected)
GeeRock2-22
The Coastal Tea Company sells 60-pound bags of blended tea to restaurants. To be able to label the tea as South Carolina Tea, at least 55% of the tea (by weight) in the bag must be Carolina grown. For quality, Coastal requires that the blend achieve an average aroma rating of at least 1.65. Carolina tea, which costs Coastal $1.80 per pound, has an aroma rating 2; other teas likely to be blended with Carolina tea are only rated at 1.2, but they are available for only $0.60 per pound. Determine the best mix of Carolina and regular tea to achieve Coastal’s blending goals, while keeping the costs as low as possible.
2-28
Treetop Hammocks produces lightweigh nylon hammocks designed for campers, scouts, and hikers. The hammocks come in two styles: double and single. The double hammocks sell for $225 each. They incur a direct labor cost of $101.25 and a production cost of $38.75 and they are packed with hanging apparatus and storage bags, which cost $20. The single hammocks sell for $175 each. Their direct labor costs are $70 and production costs are $30, and they too are packed with the same hanging apparatus and storage bags, which cost $20. Each double hammock uses 3.2 hours of production time. Treetops plans for no more than 960 labor hours per production cycle. Treetops wants to maximize its profit while making no more than 200 single hammocks and no more than 400 total hammocks per production cycle.
a. How many of each hammock should Treetops make?
b. If the restriction on single hammocks were removed, what would be the optimal production plan?
2-29
A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup of 2% milk, frothed, and 0.5 cup of whipped cream. The low-fat latte contains a shot of espresso, 1.25 cups of skim milk, frothed, and no whipped cream. The plane begins its journey with 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream. The airline makes a profit of $1.58 on each regular latte and $1.65 on each low-fat latte. Assuming that all lattes made are sold, what would be the ideal mix of regular and low-fat lattes to maximize the profit for the airline?
2-34
A plumbing manufacturer makes two lines of bathtubs, model A and model B. Every tub requires blending a certain amount of steel and zinc; the company has available a total of 24,500 pounds of steel and 6,000 pounds of zinc. Each model A bathtub requires a mixture of 120 pounds of steel and 20 pounds of zinc, and each yields a profit of $90. Each model B tub produced can be sold for a profit of $70; it requires 100 pounds of steel and 30 pounds of zinc. To maintain an adequate supply of both models, the manufacturer would like the number of model A tubs made to be no more than 5 times the number of model B tubs. Find the best product mix of bathtubs.
2-40
A photocopy machine company produces three types of laser printers; the Print Jet, the Print Desk, and the Print Pro – the sale of which earn profits of $60, $90, and $73, respectively. The Print Jet requires 2.9 hours of assembly time and 1.4 hours of testing time. The Print Desk requires 3.7 hours of assembly time and 2.1 hours of testing time. The Print Pro requires 3 hours of assembly time and 1.7 hours of testing time. The company wants to ensure the Print Desk constitutes a t least 15% of the total production and Print Jet and Print Desk together constitute at least 40% of the total production. There are 3,600 hours of assembly time and 2,000 hours of testing time available for the month. What combination of printers should be produced to maximize profits?