1. Solve the following linear program, and find the optimal value of the objective function.

Maximize 2 A + 3 B + 4 C

Subject to

A + B + C <= 20

A + B <= 15

B - C >= 4

A, B, C are non-negative

2. Consider a firm shipping salt from mines A and B to cities X, Y, and Z. The availability (tons), demands (tons) , and per unit (ton) cost of transportation are given below:

			demands
		20	25	30
availability		X	Y	Z
60	A	2	4	7
50	B	3	7	4

For example, availability at A is 60 tons, demand at Y is 25 tons, and the cost of shipping a ton from B to X is 3. (If you are uncomfortable with the cost being 3, you could think of it as a surrogate for $300. But in solving the problem, leave it as 3.)

What is the least cost of transportation? (That is, figure out how best to make the shipments, and find the total cost of that).

(Hint: decision variables are the amounts to be shipped from mines to cities. Amounts shipped from a mine should not exceed the availability; amount shipped to a city must meet the demand of that city)