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4. If the retailer wants to sell 150 PortaBoys next week, what should the price be?
5. What would the weekly sales be if the price were set at $150 per system?
Solution.
1. We recall from Section 1.5 the meaning of ‘independent’ and ‘dependent’ variable. Since x
is to be the independent variable, and p the dependent variable, we treat x as the input
variable and p as the output variable. Hence, we are looking for a function of the form
p(x) = mx + b. To determine m and b, we use the fact that 20 PortaBoys were sold during
the week the price was 220 dollars and 40 units were sold when the price was 190 dollars.
Using function notation, these two facts can be translated as p(20) = 220 and p(40) = 190.
Since m represents the rate of change of p with respect to x, we have
m= ∆p
190 − 220
−30
=
=
= −1.5.
∆x
40 − 20
20 We now have determined p(x) = −1.5x + b. To determine b, we can use our given data again.
Using p(20) = 220, we substitute x = 20 into p(x) = 1.5x + b and set the result equal to 220:
−1.5(20)...

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