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.

15 amberjack
35 flounder
minimum cost = $165