High School

3.5 Review Worksheet

3. Mountaineer Products Incorporated manufactures mountain-bike

accessories

. It is considering making a new type of reflector for night

biking. The

expense and revenue functions are E = -450p +

90,000

and R=-185p2 +9,000p.

a. Graph the two functions and find the price at the two breakeven points.

120000

b. Determine the revenue

and expense amounts for

each of the breakeven

Points

100000

-80000-

60000

c. What price will yield

the maximum revenue?

What is the max revenue

40000-

at that price?

-20000-

-50

0

60

50

100

150

3 5 Review Worksheet 3 Mountaineer Products Incorporated manufactures mountain bike accessories It is considering making a new type of reflector for night biking The

Answer :

The two functions are graphed and attached

The price at the two breakeven points are p = 12.66 and p = 38.42

The revenue and expense amounts for each break even points are 84303 and 72711

The maximum revenue is $328300 at a price of $24.32

Graphing the two functions and find the price at the two breakeven points.

From the question, we have the following parameters that can be used in our computation:

E = -450p + 90000

R = -185p² + 9000p

The price at the two breakeven points is the point where the functions intersect

The graph is added as an attachment and the price at the two breakeven points are p = 12.66 and p = 38.42

How to determine the revenue and expense amounts for each break even points

We have

p = 12.66 and p = 38.42


For the expense function, we have

E = -450 * 12.66 + 90000 = 84303

E = -450 * 38.42 + 90000 = 72711

For the revenue function, we have

R = -185 * 12.66² + 9000 * 12.66 = 84303

R = -185 * 38.42² + 9000 * 38.42 = 72711

What price will yield the maximum revenue?

Here, we have

R = -185p² + 9000p

Differentiate

R' = -370p + 9000

Set to 0

So, we have

-370p + 9000 = 0

370p = 9000

Divide

p = 24.32

This means that the maximum revenue is

Max R = 185 * 24.32² + 9000 * 24.32

Max R = 328300

Hence, the maximum revenue is $328300