The bouncy ball factory is in trouble The supervisor doesnt

The bouncy ball factory is in trouble. The supervisor doesn’t know how m nay bouncy balls to manufacture. If too many bouncy balls are manufactured, the factory will not be able to store them. If not enough bouncy balls are manufactured, the supply will not meet the demand. In this activity, you will attempt to determine the appropriate number of balls to manufacture in order to meet the demand.

George, the production supervisor, has determined that the fixed cost to produce x thousand bouncy balls is $3500, while the variable costs are $55 (for every thousand balls). Jose, the marketing manager, has determined that the optimum selling price for each bouncy ball is $0.95.

Using the information given above, determind the equation that defines production costs and determine the equation that defines revenue. Let x represent x thousand bouncy balls.

1. Production cost:_________

2. Revenue:_______________

3. Use the function above to fill out the table.

x

Costs

Revenue

0

2

4

6

8

10

4. Use the table to determine approximately how many bouncy balls should be created in order to break even.

5. About how many bouncy balls should be manufactured in order to earn a profit?

6. What is the profit function?

7. Set the profit function equal to zero and solve. Does your answer match the break-even value?

Solution

Fixed cost = $3500

Varable cost , per ball cost = $55

1) So, Production cost P(x) = 3500 +55x for x thousand balls

2) Revenue Function R(x) = x *0.95*1000 = 950x for x thousand balls

3) x P(x) R(x)

0 3500 0

2 3610 1900

4 3720 3800

6 3830 5700

8 3940 7600

10 4050 9500

4) Approximately break even is reached around 4000 balls

5) Aftre producing 4000 balls he earns profit

6) Profty function = Revenue - Cost = 950x - 3500 -55x

= 895x - 3500

7) 895x -3500 =0

x = 3.91 thousand

Yes it is aprroximateky matches with value in part 4)