Question

A fan manufacturing company produces 150 fans with a production cost of $18000 and 100 fans with a production cost of $13000. Assume that the relationship between the production cost and number of fans produced is linear.

1 find the equation of the relation ship
2 how much does the production of one fan add to the total production cost?
3 what should be the selling price of the fan in order for the company to earn a profit of $ 19000 on 500 fans
4 find the break event point of the company
5 what should be the fixed cost if company want to earn at least $15300 on 400 fans.?

Answer 1

You can think of number of fans as the x-value and the production cost as the y-values. They say the relationship is linear which means it is a straight line. You are given two points on the line: (150, 180000) and (100, 13000). Can you find the slope of the line?

Answer 2

the slope of the line will be y=500x-57000?

Answer 3

Slope \(m = \large \frac{y_2-y_1}{x_2-x_1} = \frac{18000-13000}{150-100} = ?\)

Answer 4

M= 500

Answer 5

How are you getting 500? Can you show the work?

Answer 6

Sorry, I did wrong in my paper.. is 100.

Answer 7

Yes. So y = 100x + b.
It passes through the point (100, 13000). Find b.

Answer 8

y=mx+b
18000=100(150)+b
b= 3000

Answer 9

Yes. 1) y = 100x + 3000 is the equation.

Answer 10

2) how much does the production of one fan add to the total production cost?

Slope = rise / run. If the run is 1, then slope = rise.
So if the x value, which is the number of fans, increases by 1, the y value, which is the production cost, will increase by slope which is 100.

So the production cost will go up by $100 to produce one extra fan.

Answer 11

3) 3 what should be the selling price of the fan in order for the company to earn a profit of $ 19000 on 500 fans?

First find the production cost for making 500 fans by plugging x = 500 into the equation. Then add $19,000 profit to find the selling cost.

Answer 12

the selling price will be $34000.

Answer 13

I am getting a different number. Show your work.

Answer 14

y=100(500)+3000
y= 53000
then add 19000
it should be 72000.

Answer 15

Yes, $72,000.

Answer 16

4) Not sure how to find the break-even point without the revenue function. Is the revenue mentioned anywhere in the problem that you forgot to include?

Answer 17

the revenue function will 100x
r(x)= 100x

Answer 18

Break-even point is when the cost function = revenue function
Equate the two and solve for x.

Answer 19

no. something is not right.

Answer 20

ya.. because the cost function is 100x+3000

Answer 21

where did you get the revenue function from?

Answer 22

i see my notes.. not from the question.

Answer 23

you have to run 4 and 5 by your teacher as some info seems to be missing in the problem you posted.

Answer 24

ok.. thanks for your help =D

Answer 25

you are welcome.