75 Cost The RideEm Bicycles factory can produce 100 bicy cle

75. Cost The RideEm Bicycles factory can produce 100 bicy- cles in a day at a total cost of $10,500 and it can produce 120 bicycles in a day at a total cost of $11,000. What are the company\'s daily fixed costs, and what is the marginal cos per bicycle? HINT [See Example 3

Solution

Company\'s daily fixed cost and the marginal cost per bicycle can be expressed by following linear cost function

Y = b X + a

Where,

Y is total cost of production

X is number of bicycle produced daily

b is the slope of linear cost function and it is marginal cost of bicycle, it can be calculated with following formula

Slope b = (Y2 – Y1)/ (X2 – X1)

a is intercept of linear cost function and it is fixed cost of production, it can be calculated with following formula

And Intercept a = Y1 – bX1

We know that, Y1 = $10,500 when X1 = 100 bicycles

And Y2 = $11,000 when X2 = 120 bicycles

Therefore, Slope b = ($11,000 – $10,500)/ (120 – 100)

b = $500 /20 = $25

Therefore marginal cost of per bicycle is $25.

And Intercept a = Y1 – b X1 = $10,500 - $25 * 100 = $10,500 - $2,500 = $8,000

Therefore Company\'s daily fixed cost is $8,000.