Answer to Question #326618 in Operations Research for Fionna

Question

RB Music Store assembles stereo equipment for resale in the shop. The store offers two products; two products; turntables and cassette players. The store makes a profit of P400 on each turntable and P250 on each cassette. Both must go through two steps-assembly and bench checking. A turntable takes qw hours to assemble and 4 hours to bench check. A cassette player takes 4 hours to assemble but 8 hours to bench check. Looking at this month’s schedule, the store sees that it has 60 assembly hours uncommitted and 40 hours bench-cutting time available. What combination of turntables and cassette players would maximize the store’s profit for the month?

Answer 1

Let $x_1$ - number of turntables, and $x_2$ - number of cassette players.

$\phi=400x_1+250x_2 \to max$

$\begin{cases} 14x_1+4x_2\leq60\\ 4x_1+4x_2\leq40 \end{cases}$

Let 's build graphs of the resulting equations:

The answer to our problem will be at point C:

$\begin{cases} 14x_1+4x_2=60\\ 4x_1+4x_2=40 \end{cases}\implies\begin{cases} x_1=2\\x_2 = 8 \end{cases}$

$\phi=400*2+8*250=2800$

Answer: 2 turntables and 8 cassette players.