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?
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.