Question

The cost for system 1 of dispensing maps is:

Y = 0.2 X + 6000, where Y = Total Costs in $, X=total number of maps dispensed (in a year).At 3000 maps per year, what is the marginal cost and what is the average cost?
[Tip: marginal cost means what is your additional cost by dispensing one more map. average cost means what is the cost per one map [for 3000 maps total]]

Answer 1

a. The marginal cost is $0.2.

b. The average cost is $2.20.

Step-by-step explanation:

Given in the question are the following:

Y = 0.2X + 6000 ................ (1)

Where; Y = Total Costs in $

X = total number of maps dispensed (in a year)

a. What is the marginal cost?

The marginal cost (MC) can be obtained by differentiating equation (1) with respect to X as follows:

MC = dY/dX = 0.2

Therefore, the marginal cost is $0.2.

b. What is the average cost?

This can be calculated as follows:

At X = 3000 maps

Substitute X = 3000 into equation (1) in part a to obtain the total cost as follows:

Y = 0.2(3000) + 6000

Y = (0.2 * 3000) + 6000

Y = 600 + 6000

Y = $6,600

The average cost now be calculated using the following formula:

Average cost = Y / X ...................... (2)

Where;

Y = Total Costs in $ = $6,600

X = Number of maps per year = 3,000

Substituting the values into equation (2), we have:

Average cost = $6,600 / 3,000 = $2.20

Therefore, the average cost is $2.20.