Question

1. The Academic T-Shirt Company did a cost study and found that it costs $1400 to produce 600 “I Love Math” T-shirts. The total cost is $1600 for a volume of 700 T-shirts.

Determine the linear cost-volume function.

What is the fixed cost?

What is the unit cost?

2. The Computer Shop sells computers. The shop has a fixed cost of $1500 per week. Its average cost per computer is $649, and the average selling price is $899 each.

Write the linear cost function.

Write the linear revenue function.

Find the cost of selling 37 computers per week.

Find the revenue from selling 37 computers.

Find the break-even point.

3. If a product has a selling price of $518, consumers are willing to buy 90 units of it. If the price is $265, they will buy 200 units. A manufacturer will produce 100 units of the product if the selling price is $250 or 210 units if the selling price is $382.

Find the demand equation.

Find the supply equation.

At what price would manufacturers produce 150 units of the product?

At what price would consumers buy 175 units of the product?

Find the market equilibrium point (both price and quantity).

Answer 1

1) let linear cost volume function is

C(x) = mx + b

we have two points

( 600 , 1400 ) and ( 700 , 1600 )

slope = ( 1600 - 1400 ) / ( 700 - 600 )

slope = 2

applying point slope form

y - 1400 = 2 ( x - 600 )

y = 2x + 200

hence, cost volume function is

C(x) = 2x + 200

where C(x) = cost , x = volume of t- shirts

2) linear cost function is

C(x) = 649x + 1500

linear revenue function is

R(x) = 899x

cost of selling 39 computers

C(x) = 649(37) + 1500

C(x) = $ 25513

revenue from selling 37 computers

R(x) = $ 33263

break even point is

649x + 1500 = 899x

x = 6