Question

A company sells one of its products for $44 each. The monthly fixed costs are $2900. The marginal cost of the product is$10. Let q = quantity and C(q) = cost.b) Express the total monthly revenue, R, as a function of the quantity, q, sold each month.R (q) = c) Find the quantity, q, produced and sold each month at which this company will break even. Round your answer to a whole number.q =

Answer 1

*5 items sold in a mionth will result in break even.

Explanation:

The monthly revenue, R, for the item that sells for $44/item is the product of the price ($44/each) and the quantity, q, sold in one month.

R/month = ($44/item)*q(items/month), or

R = 44q for one month.

Fixed monthly costs are $2900. The fixed monthly costs per item would be:

If q is for one month,

Fixed Costs/month/item = $2900/q

Marginal Costs/month = $10*q [q is for one month]

The net revenue, or profit, P, for each item would be:

P = $44 - $2900/q - $10

P = $34 - $2900/q

For one month, if q items are sold, the net profit, P, would be:

P (1 moth, q items sold) = q*($34 - $2900/q)

P (1 month) = $34q - $2900

Breakeven means P = $0

P (1 month): 0 = q*($34 - $2900/q)

34q - 2900 = 0

34q = 2900

q = 85.3 or 85 items

Check:

Will sales of 85 itmes for $44 each result in break even profit (P = 0)?

P(q) = q*($34 - $2900/q)

P(85) = 85*($34) - $2900 ?

P(85) = $2890 - $2900

P(85) = $10 Close to breakeven YES

YES. The numbers are not exact, due to the rounding from 85.3 to 85 items

Note: [85.3 itmes would be ($2900 - $28900]