solution

Say a company produces bowls (b) and mugs (m) and the goal is to

Maximize profit = 70b + 50m where 70 is the profit per unit on bowls and 50 is the profit per unit on mugs.

In production there are only 40 hours of labor available and each bowl takes an hour of labor and each mug takes 2 hours of labor. So, for labor we have constraint

Labor constraint 1b + 2m = 40.

Also in production there are only 120 pounds of clay available and each bowl takes 4 pounds of clay and each mug takes 3 pounds of clay. So, for clay we have constraint

Clay constraint 4b + 3m = 120

The non-negativity constraints are b = 0 and m = 0.

Let’s say bowls are on the horizontal axis and mugs are on the vertical axis. Remember each combination of bowls and mugs, or point in the graph has form (b, m), where the number of bowls is the first number and the number of mugs is the second number.