Question

BREAK-EVEN ANALYSIS

1. The quantity for a 17-inch LCD TV is 20,000 at a price of Php25,000, while 45,000 is demanded for the price of Php15,000. Assuming a linear relationship between price and quantity, which of the following models the price-quantity function of the LCD TV?

2. A young entrepreneur is willing to supply 60 pieces of personalized baller band at a price of Php80 and 100 at a price of Php110. Assuming a linear relationship between price and quantity, which of the following models the price-quantity function of the baller band?

3. Suppose that the demand function for a certain brand of shampoo is D(x) = -1.25x + 525. What is the highest price anyone will be willing to pay for the shampoo?

4. The cost and revenue function for a particular brand of bag are C(x) = 6x + 3 and R(x) = 19 - 2x. What is the break even point?

5.Let the supply and demand functions for yogurt ice cream be given by S(x) = 0.4x and D(x) = 100 - 0.4x, respectively. What is the equilibrium quantity and price?

6-8. The financial research department of a company that manufactures earphones determine its cost function as C(x) = 120x + 3900. The company sells the earphone at Php250 each.  

6.            How many earphones must be sold to realize a profit of Php150,020?

7.            What is the profit from the sale of 250 units?

8.            What is the break-even quantity?  '

9-10 A baker sells her cakes at Php 285 per piece selling all that she produces. Her fixed cost is Php 4,500 and her variable cost is Php 92 per piece.

9. With how many cakes will she break even?

10. With how many cakes will she enjoy a profit of Php 5,000? A loss of Php 1,000?

Answer 1

All prices mentioned below are in Php

1)

q = 20,000 and P = 25,000

q = 45,000 and P = 15,000

Hence we apply the two point formula for finding the demand function:

Demand function: P = 33,000 - (2q/5)

2)

q = 60 and P = 80

q = 100 and P = 110

Hence we apply two point formula for finding the supply function:

Supply function: P = 35 + (3q/4)

3)

D(x) = -1.25x + 525.

where x = price

The highest price x is when D(x) = 0

-1.25x + 525 = 0

1.25x = 525

x = 420 = Price

4)

C(x) = 6x+3

R(x) = 19-2x

where x = quantity

For breakeven, C(x) = R(x)

6x +3 = 19-2x

8x = 16

x = 2 = Breakeven quantity

5)

S(x) = 0.4x

D(x) = 100 - 0.4x

where x = price

For equilibrium,

S(x) = D(x)

0.4x = 100 - 0.4x

0.8x = 100

x = 125 = Equilibrium price

S(x) = Equilibrium quantity = 0.4x = 50

6)

C(x) = 120x + 3900

where x = quantity

Price P = 250

Profit = Total revenue - Total costs

Profits = P*x - 120x - 3900

Profits = 250x - 120x - 3900

Profits = 130x - 3900

150020 = 130x - 3900

153,920 = 130x

x = 1184 = No. of earphones to be sold to earn a profit of 150,020

7)

Quantity sold = x = 250

Proftis = 130x - 3900

Profits = 130*250 - 3900

Profits = 28,600

8)

For breakeven, profits = 0

130x - 3900 = 0

x = 3900/130 = 30 = Breakeven quantity

9)

Let x =Quantity of cakes

Price = P = 285

Fixed Costs = FC = 4500

Variable Costs = VC = 92x

Total costs = TC = FC + VC = 92x + 4500

Total revenue = TR = P*x = 285x

For breakeven; TR = TC

285x = 92x + 4500

193x = 4500

x = 23.316 cakes for breakeven

10)

Profits = TR - TC = 193x - 4500

For profits = 5000,

193x - 4500 = 5000

193x = 9500

x = 49.223 cakes required for profits of 5000

For loss of 1000,

-1000 = 193x - 4500

193x = 3500

x = 18.135 cakes to be sold to incur a loss of 1000