Question

TMI, a manufacturer of blank DVDs, has a monthly fixed cost of $14,200 and a variable cost of 70 cents/disc.

Find a function C that gives the total cost incurred by TMI in the manufacture of x discs/month, in dollars; C(x).

Answer 1

The total cost function C(x) for the manufacturer TMI, which includes both fixed costs and variable costs, is C(x) = $14,200 + ($0.70 × x), where x is the number of discs produced per month.

Step-by-step explanation:

The student is asking for a function C(x) that represents the total cost incurred by TMI in the manufacture of x discs per month. To find the total cost function, we need to take into account both the fixed costs and the variable costs. The fixed cost, which doesn't change regardless of the number of discs produced, is $14,200 per month. The variable cost is the cost that changes with the number of discs produced, which is 70 cents (or $0.70) per disc. Therefore, the function for total cost C(x) is given by:

C(x) = Fixed Costs + (Variable Cost per disc x Number of discs)

C(x) = $14,200 + ($0.70 × x)

Answer 2

Answer: Therefore, the total cost incurred per month is;

C(x) = 14,200 + 0.7x dollars

Step-by-step explanation:

Given;

Fixed cost Cf = $14,200 per month

variable cost = 70cent/disc

Number of disc manufactured per month = x disc/month.

The total variable cost in a month can be given as;

Cv = 70cent/disc × x disc/month

Cv = 70x cent/month × 1/100cent/dollar

Cv = 0.7x dollar/month

Total cost C = Fixed cost + variable cost

C = Cf + Cv

Substituting the values, we have;

C(x) = 14,200 + 0.7x dollars/month