Question

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?

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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

5. Equilibrium quantity and price will be

S(x)= D(x) ie 0.4x = 100 - 0.4x

So, x = 125

Hence price is php 125 and quantity is 100 -0.4(125) = 50.

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Cost fucntion => 120x +3900

So, contribution per unit => 250-120 = 130

6.

Desired profit	150,020
Fixed expenses	3900
Total required contribution (a)	153,920
Contribution per unit (b)	130
Hence units told be sold (A/B)	1,184

7.

250 units sold.

Total contribution (130×250)	32,500
Less: Fixed costs	3,900
profits	29,600

8.

Break even quantity => fixed costs/contribution per unit ie 3900/130 = 30 units

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Contribution per unit = 285 -92 = 193

9. BEP = 4500/193 = 23.22 or 23 unit

10.

• 5000 profit, so (4500+5000)/193 = 49.22 or 49 units.
• 1000 loss, so (4500-1000)/193 19 = 18.13 or 18 units