Linear Programming Math Example 4

Follow the full solution, then compare it with the other examples linked below.

medium

A company makes chairs (

\

profit) and tables (

70

profit). Each chair takes 2 hours, each table takes 5 hours. With 40 hours available, maximize profit.

1
Let $c$ = chairs, $t$ = tables. Maximize $P = 40c + 70t$ subject to $2c + 5t \leq 40$ , $c, t \geq 0$ .
2
Vertices: $(0,0)$ , $(20,0)$ , $(0,8)$ . Profits: $0$ , $800$ , $560$ . Maximum: $P = 800$ at 20 chairs.

Answer

\

800$ with 20 chairs and 0 tables

Real-world linear programming models resources as constraints and profit as the objective. Here the chair has better profit-per-hour (

\

/hr vs

14

/hr), so producing only chairs is optimal.

About Linear Programming

Linear programming optimizes a linear objective subject to linear inequality or equality constraints.

Maximize [formula] subject to [formula], [formula], [formula].

Minimize [formula] subject to [formula], [formula], [formula], [formula].

A feasible region has vertices at [formula], [formula], [formula], [formula]. Maximize [formula].