Question

A plane delivers two types of cargo between two destinations. Each crate of cargo I is 7 cubic feet in volume and 131 pounds in weight, and earns $20 in revenue. Each crate of cargo II is 7 cubic feet in volume and 262 pounds in weight, and earns $25 in revenue. The plane has available at most 525 cubic feet and 12,576 pounds for the crates. Finally, at least twice the number of crates of I as II must be shipped. Find the number of crates of each cargo to ship in order to maximize revenue. Find the maximum revenue.

crates of cargo I ______
crates of cargo II________
maximum revenue________		$

Answer 1

Let, the number of crates of cargo 1 is x

Let, the number of crates of cargo 2 is y

Weight of x crates of cargo 1 is 131x

Weight of y crates of cargo 2 is 262y

Total weight available for the crates in the plane is 12576 impies

Volume of x crates of cargo 1 is 7x

Weight of y crates of cargo 2 is 7y

Total volume available for the crates in the plane is 525 implies

Twice the number of crates of 1 as 2 must be shipped implies

The revenue generate by the ship is

Plot the above inequalities and plot the feasible region

The feasible region is the quadrilateral OABC

The optimal solution to a linear programming occurs at a corner point to the feasible region or along a line connecting two adjacent corner points of the feasible region. If a feasible region is bounded, there will always be an optimal solution.

Find the value of f(x,y) at the corner points A, B, C

From above the maximum revenue is 1605 and occurs for x=54 (Crate 1) and y=21 (Crate 2)