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Problem Set 2: Linear Programming
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Question 49
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Laura runs a factory that makes stereo tuners. Each R80 takes 6 ounces of plastic and 4 ounces of metal.
Each D200 requires 3 ounces of plastic and 6 ounces of metal. The factory has 174 ounces of plastic, 252
ounces of metal available, with a maximum of 18 R80 that can be built each week. If each R80 generates
$10 in profit, and each D200 generates $1, how many of each of the stereo tuners should Laura have the
factory make each week to make the most profit?
R80:
D200:
Best profit:

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

36

step-by-step explanation:

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get