Question

A profit formula for dining plates from the previous year was modeled by the function P(d) = –15d2 + 1,200d – 2,000. The manufacturer noticed an increase in the number of units sold by 50% the next year, which can be modeled by the function l(d) = 1.5d.
Which composite function can be used to find the new profit formula after the increase in the number of units?

Answer 1

Answer:

$P(d)=-33.75d^2+1800d-2000$

Step-by-step explanation:

The profit function is:

$P(d) = -15d^2+1,200d-2,000$

Where

P is the profit

and

d is the number of units sold

Now, there is a 50% increase in number of units sold, so d will become:

50% = 50/100 = 0.5

d + 0.5d = 1.5d

So, we have to replace "d" with "1.5d" in the function, which makes it:

$P(d) = -15d^2+1,200d-2,000\\P(d) = -15(1.5d)^2+1,200(1.5d)-2,000\\P(d)=-15(33.75)d^2+1800d-2000\\P(d)=-33.75d^2+1800d-2000$

From the equations shown, last answer choice is correct.

$P(d)=-33.75d^2+1800d-2000$