Question

Break-Even Analysis

A multimedia company produces DVDs. It estimates their cost function to be:

C(x)=13.2 x+48,038

The DVD is sold to retail outlets and the revenue function is:

R(x)=16.61 x

Both C(x) and R(x) are in dollars and x= number of DVDs manufactured and sold.

How many DVDs must be manufactured and sold in order for the company to break even? (Round to the nearest whole number).

Equilibrium Analysis

Suppose that the demand function and supply function for honey are P=D(q)=-1.3 q+23 and

P=S(q)=0.5 q+2.9

where P is the price in dollars for an 8-oz container and q is the quantity in 8-oz containers.

Find the equilibrium quantity. (Round to the nearest whole number).

Answer 1

Part 1

Let the break even quantity be x units

Cost function = C(x) = 13.2x + 48,038

Revenue function = R(x) = 16.61x

At the break even quantity, cost is same as revenue

13.2x + 48,038 = 16.61x

16.61x - 13.2x = 48,038

3.41x = 48,038

x = 14,087

Hence, 14,087 DVDs must be manufactured and sold.

Part 2

Demand function = D(q) = - 1.3q + 23

Supply function = S(q) = 0.5q + 2.9

At the equilibrium level, quantity demanded and supplied are same.

Hence, D(q) = S(q)

- 1.3q + 23 = 0.5q + 2.9

0.5q + 1.3q = 23 - 2.9

1.8q = 20.1

q = 11 units

Hence, equilibrium quantity = 11 units

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