Question

The monthly revenue achieved by selling x wristwatches is figured to be x(40-0.2x)dollars. The wholesale cost of each watch is $32.
a. How many watches need to be sold each month to achieve a profit (revenue-cost) of $50?

for this part I did
x(40-.2x)-32x=50

I got 99.5 so I rounded it to 100

I'm not sure if a is right and I can't figure how to do b and c.

Perhaps for b you do the vertex -b/2a?
but I get 30 which can't be right.

b. What is the maximum revenue this firm can earn?

c. How many wristwatches should the firm sell to maximize profit?

Answer 1

first of all, 100 can't be right.
100(40-20) - 32(100) = -1200 and not 50

You would be solving
-.2x^2 +8x - 50 = 0
multiply by -5
x^2 - 40x + 250 = 0
x = 32.25 or x = 7.75 OR 32 or 8

check: if x=8
8(40-.2(8)) - 32(8) = 51.2 close enough
if x = 32
32(40-.2(32)) - 32(32) = 51.2 , ok



Your profit equation is
Profit = x(40 - .2x) - 32x
= -.2x^2 + 8x

You are probably studying the parabola.
isn't the above a parabola opening downwards?
Wouldn't the vertex give you all the information you need?

What method have you learned to find the vertex ?

Answer 2

Perhaps for b you do the vertex -b/2a?
but I get 30 is that right?

Answer 3

I can't understand how part a. could be either 8 or 32. How could it be more than one answer?

Answer 4

if your profit function is
-.2x^2 + 8x
then the value of -b/(2a) = -8/(2(-.2)) = 20 (you had 30)

then if x=20
maximum profit = 20(40 - .2(20) - 32(20) = 80

As to your last question, doesn't every parabola have the same y value for 2 different x values, except the x value of the vertex ?

Didn't I show above that both 8 and 32 produce a profit of appr. 50 ??