Question

A marginal cost function is given by C' (q) = √√√9+ 10 dollars per unit. If the fixed cost is

$1200, find the total cost of producing 36 units.
Select one:
$216
$504
$1216
$1704

Answer 1

The total cost of producing 36 units is $2064.

Step-by-step explanation:

To find the total cost of producing 36 units, we need to calculate the total cost function. The marginal cost function, C'(q), is given as √√√9 + 10 dollars per unit. The fixed cost is $1200.

The total cost function, C(q), can be found by integrating the marginal cost function. Integrating √√√9 + 10 gives us (3/4)q^(3/4) + 10q + C, where C is the constant of integration.

To find C, we can use the information that the total cost is $1200 when q is 0. Substituting these values, we get (3/4)(0)^(3/4) + 10(0) + C = 1200. This simplifies to C = 1200.

So the total cost function is C(q) = (3/4)q^(3/4) + 10q + 1200. To find the total cost of producing 36 units, we substitute q = 36 into the equation: C(36) = (3/4)(36)^(3/4) + 10(36) + 1200 = 504 + 360 + 1200 = 2064 dollars.