Answer:
*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]