A truck traveling from New York to Baltimore is to be loaded with two types of cargo. Each crate of cargo A is 4 cubic feet in volume, weighs 100 pounds, and earns $13 for the driver. Each crate of cargo B is 3 cubic feet in volume, weighs 200 pounds, and earns $9 for the driver. The truck can carry no more than 300 cubic feet of crates and no more than 10,000 pounds. Also, the number of crates of cargo B must be less than or equal to twice the number of crates of cargo A.
(a) Fill in the following chart.

(b) Let x be the number of crates of cargo A and y the number of crates of cargo B. Referring to the chart, give the two inequalities that x and y must satisfy because of the truck's capacity for volume and weight.
(c) Give the inequalities that x and y must satisfy because of the last sentence of the problem and also because x and y cannot be negative.
(d) Express the total earnings from carrying x crates of cargo A and y crates of cargo B.
(e) Graph the feasible set for the shipping problem.

Transcribed Image Text:

Truck Capacity Volume Weight Earnings