Question

Math 30 Lab Assignment 1 1 OG Music produces G-pods, devices that hold 1GB of music. G-pods sell to the customer for S10 each and have fixed costs of $2000 and variable costs of $3.50 per G-pod. Letc, d, and p be the variables for cost, demand, and price, respectively. a. What is the cost function? b. What is the revenue function? c. What is the profit function? d. What is the break-even point? (Recall that break even means cost revenue, or profit-0) e. The company set a goal of $10000, how many G-pods do they need to sell in order to reach that goal?

Answer 1

Fixed costs (a) = $2,000

Variable cost per unit (b) = $3.50

Selling price per unit (k) = $10

Number of units sold = X

a)

Cost function: C = a + bX

= 2,000 + 3.50X

b)

Revenue function: d = kX

= 10X

c)

Profit function: p = Revenue function - Cost function

= 10X - 2,000 - 3.50X

= 6.50X - 2,000

d)

At break even point, cost and revenues are equal.

2,000 + 3.50X = 10X

6.5X = 2,000

X = 308 (ROUNDED TO NEAREST WHOLE NUMBER)

Hence, break even will occur, when 308 units are sold.

e)

Target profit = $10,000

Let the number of units o be sold be X

Profit function: p = 6.50X - 2,000

10,000 = 6.50X - 2,000

6.50X = 12,000

X = 1,847 (rounded to next whole number)

Hence, 1,847 G-Pods are needed to be sold to earn a profit of $10,000

Please ask if you have any query related to the question. Thank you