Question

The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.

a. Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. Be sure to state the units you use.
b. Express using functional notation the total cost if there are 250 widgets produced in a month, and then calculate that value.

Answer 1

The total cost C of a manufacturer in a month, as a function of the number of widgets produced, is C(N) = Fixed Costs + (Variable Cost per Unit × N). For 250 widgets with a variable cost of $80 per widget and fixed costs of $160, the total cost is $20,160.

Step-by-step explanation:

To express the total cost C of a manufacturer in a month as a function of the number of widgets produced, we use the formula: C(N) = Fixed Costs + (Variable Cost per Unit × N), where N is the number of widgets. Assuming the fixed costs are $160 and the variable cost per unit is known, this formula can be applied.

For part b, if we know the variable cost per widget is $80, and the manufacturer produces 250 widgets, we can express the total cost function as C(250) = 160 + (80 × 250). To calculate the cost for 250 widgets, we multiply 80 by 250 and add the fixed costs of $160, which results in C(250) = 160 + 20000 = 20160.

Answer 2

(a) C = 9000 + 15N

(b) Cost of 250 widgets is $12750

Step-by-step explanation:

The question has missing details. See attachment for complete question

Solving (a): An expression for total cost.

The expression is generated using:

`Total\ Cost = Fixed\ Cost + Variable\ Cost * Number\ of\ Items`

From the given parameters:

`Fixed\ Cost = 9000`

`Variable\ Cost = 15`

`Number\ of\ Items = N`

So, the expression becomes:

`C = 9000 + 15 * N`

`C = 9000 + 15 N`

Solving (b): Cost of 250 widgets

In this case:

`N =250`

Substitute 250 for N in
`C = 9000 + 15 N`

`C = 9000 + 15 * 250`

`C = 9000 + 3750`

`C = 12750`