Question

A clothing shop makes suits and blazers. Three main resources are used: material, rack space, and labor. The shop has developed this linear programming model for determining the number of suits

and blazers to make ( and ) to maximize profits

maximize Z = 100x1 + 150x2 (profit, $)

Subject to

10x1 + 20x2 smaller than or equal to 300 (material, yd.2

)

x1 + x2 smaller than or equal to 20 (rack space)

10x1 + 4x2 smaller than or equal to160 (labor, hr.)

x1, x2 bigger than or equal to 0

Answer 1

$\begin{cases} 10x_1+20x_2\leq 300, \\ x_1+x_2\leq 20,\\ 10x_1+4x_2\leq 160; \end{cases}$

$Z=100x_1+150x_2\to max,$

$\begin{cases} x_1+x_2\leq 20, \\ 10x_1+20x_2\leq 300; \end{cases}$

$\begin{cases} x_1=10, \\ x_2=10; \end{cases}$

$Z=100\cdot 10+150\cdot 10=2500$ $.