3. A seafood restaurant owner orders at least 50 fish. He cannot use more than 30 amberjack or more than 35 flounder. Amberjack costs $4 each and flounder costs $3 each. How many of each fish should he use the minimize his cost?

Refer to the figure shown below.

Let x = the number of amberjacks

Let y = the number of flounder

Because amberjack costs $4 each and flounder costs $3 each, the cost function is

C = 4x + 3y

The number of fish is at least 50, therefore

x + y ≥ 50

There should be no more than 30 amberjacks and or no more than 35 flounder, therefore

x ≤ 30

y ≤ 35

The solution region for the inequalities is shown shaded. Optimum values of the cost function occur at the vertices.

The minimum cost occurs at (15,35) and it is C = 4*15 + 3*35 = $165.

Answer:

15 amberjack

35 flounder

minimum cost = $165