Question

A company produces and sells hair dryers in a market where price (p) and demand (D) are related follows: p = $35+ (3,000)/D-(4,800)/D2 The fixed cost (Ct) is $800 per month and the variable cost per hair dryer (c.) is $38. - Add to % E Q

With reference to the company in Question 1, assume price and demand are unrelated. The company sells the hair dryers for $80 each if they spend $8,000 per month on advertising (C.). CF and c, remain as indicated in Question 1. The maximum production capacity is 5,000 hair dryers per month.
a) What is the demand breakeven point?
b) Is the company's demand breakeven point (in %) more sensitive to 10% increase in sales price or 20% reduction in variable costs? Explain your answer.

Answer 1

Step-by-step explanation:

Given that:

`p = 35 + (3000)/(D)- (4800)/(D^2)`

The total revenue = p × D

∴

multiplying both sides by D; we have:

`p* D = 35 * D + (3000)/(D) * D- (4800)/(D^2)* D`

`= 35 D +3000}{D} - (4800)/(D)`

The total cost = (Per unit Variable cost × D) + Advertising cost

The total cost = 38D + 8000

The selling price = 80

From D units, the total revenue = 80D

∴

The break-even will take place when total revenue equals total cost.

So;

8000 + 38D = 80D

8000 = 80 D - 38D

8000 =42D

D = 8000/42

D = 190.48

(b)

Suppose the new sales price

Then;

8000 + 38D = 88D

8000 = 88D - 38D

8000 = 50D

D = 160

Hence, the break-even decreases by:

`\Big((190.48-160)/(190.48)* 100\Big) = 16\%`

However; suppose the variable cost = 30.4

Then;

8000 + 30.4D = 80D

8000 = 80D - 30.4D

8000 = 49.6D

D = 8000/49.6

D = 161.29

Therefore;

This implies that the break-even decreased by:

`\Big((190.48-161.29)/(190.48)* 100\Big) = 15.32\%`

Hence, the break-even is more likely to change by 10% in its selling price.