Question #326618

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?


1
Expert's answer
2022-04-11T15:08:07-0400

Let x1x_1 - number of turntables, and x2x_2 - number of cassette players.

ϕ=400x1+250x2max\phi=400x_1+250x_2 \to max

{14x1+4x2604x1+4x240\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:

{14x1+4x2=604x1+4x2=40    {x1=2x2=8\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}

ϕ=4002+8250=2800\phi=400*2+8*250=2800

Answer: 2 turntables and 8 cassette players.


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