# I have no idea what to do.

• October 7th 2009, 07:10 PM
MathBane
I have no idea what to do.
The question:

(a) Use the formula $53N-(40N+1725)$ to determine the two break-even points for this manufacturer. Assume here that the manufacturer produces the widgets in blocks of 50, so a table setup showing N in multiples of 50 is appropriate.

____widgets/mo (smaller value)
____widgets/mo (larger value)

(b) Use the formula $53N-(40N+1725)$ to determine the production level at which profit is maximized if the manufacturer can produce at most 1500 widgets in a month. As in part (a), assume that the manufacturer produces the widgets in blocks of 50.

____

This one got me stumped. When I put it in, I get a straight line going to infinity... I was expecting a parabola because it mentioned two break even points. I must be missing something important here.
• October 7th 2009, 08:22 PM
pacman
your equation is linear in form, can you post the entire problem? (Wait)
• October 8th 2009, 03:45 AM
MathBane
Quote:

your equation is linear in form, can you post the entire problem? (Wait)
Sure thing:

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.

The total revenue R 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 revenue, we need to know the selling price per unit of the item. To find the total revenue, we multiply this selling price by the number of items produced.

The profit P for a manufacturer is the total revenue minus the total cost. If this number is positive, then the manufacturer turns a profit, whereas if this number is negative, then the manufacturer has a loss. If the profit is zero, then the manufacturer is at a break-even point.

A manufacturer of widgets has fixed costs of \$1725 per month, and the variable cost is \$40 per widget (so it costs \$40 to produce 1 widget). Let N be the number of widgets produced in a month.

-EDIT-

A manufacturer of widgets has fixed costs of \$150 per widget (so it costs \$50 to produce 1 widget). Let N be the number of widgets produced in a month.

a. Find a formula for the manufacturer's total cost C as a function of N.

$C=55N+200$

b. The manufacturer sells the widgets for \$65 each. FInd a formula for the total revenue R as a function of N.

$R=58N$

c. Use your answers to parts a and b to find a formula for the profit P of this manufacturer as a function of N.

$P=58N-(55N+200)$ or equivalently $3N-200$.

d. Use your formula from part c to determine the break-even point for this manufacturer.

66.67 widgets per month

It doesn't help me much... I don't know how they got 66.67 and why the math problem I'm having trouble with has two break even points and not just one.