Question

If a retail store has fixed cost of $150 and variable cost of $175 per unit and sell its product at

$500 per unit. (8 Marks)

a. Find the cost function

b. Find revenue function.

c. Find profit function.

d. Find break-even level of output.​

Answer 1

Answer:

) A small home business is set up with an investment of $10,000 for equipment. The business manufactures a product at a cost of $0.65 per unit. If the product sells for $1.20, how many units must be sold before the business breaks even?

2) A person setting up a part-time business makes an initial investment of $5,000. The unit cost of the product is $21.60, and the selling price is $34.10.

a) Find equations for the total cost C and total revenues R for x units.

b) Find the break-even point.

3) A manufacturing company determines the total cost in dollars of producing x units of a certain product is $25 per unit plus a fixed cost of $3500. Find the equation of the cost, graph it, find the y-intercept and the slope.

*4) In a manufacturer, the cost of producing 20 flashlights per week is $200 while the cost of producing 100 flashlights per week is $600.

a) Find the equation for the cost.

b) Find the cost of producing 150 flashlights per week.

c) What is the manufacturer fixed cost?

*5) A contractor purchases a piece of equipment for $26,500. The equipment requires an average expenditure of $5.25 per hour for fuel and maintenance, and the operator is paid $9.50 per hour.

a) Find a linear equation giving the total cost C of operating this equipment t hours.

b) Given that customers are charged $25 per hour of machine use, write an equation for the revenue R derived from t hours of use.

c) Use the formula (P=R-C) to write an equation for the profit derived from t hours of use.

d) Find the number of hours the equipment must be operated for the contractor to break even.

6) Suppose the cost for a product is $2.50 per unit with a fixed cost of $1200. If the selling price per unit is $10, how many units must be produced to break even? (graph the equations and show the intersection point)

B7) Use the data in the table below to solve the following problem. (R-value of insulation is a measure of its ability to resist heat transfer, higher R-value means higher insulation)

a) Write linear equations relating the R-value to the thickness in inches for fiberglass insulation and cellulose fiber.

b) Use the costs per cubic inch to determine which product costs less and provides an R-value of 24.

Thickness (in) R-value Cost/cubic inch $

Fiberglass 3.5 11 0.21

6 19

Cellulose 3.5 13 0.33

6 22