Question

Suppose that the cost of producing x units, C(x), is a linear function. Furthermore, it is known the marginal cost is $1.50 and that the cost of producing 50 units is $2,275.

a) Determine a formula for C(x)

b) Determine the fixed cost

Answer 1

Given that C(x) is a linear function,

Cost of producing 50 units = 2,275

this includes fixed cost and variable costs. So, we have to find fixed cost of equipment and variable cost of producing each of the 50 items.

Marginal cost = 1.50

This marginal cost indicates the increase in total production cost if we increase output by 1 unit.

So, for producing 1 unit, the variable cost is 1.50

Implies, for producing 50 units, the variable cost is = 50X1.5 = 75

So, the total cost = fixed cost + variable cost

implies, 2275 = fixed cost+75

Fixed cost = 2200.

Cost function C(x) = 2200+1.75x

where, x is units of production.