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
