A grocer bought 300 pounds of bananas at 30 cents per pound. Experience at this store indicates that, as a result of aging, 30% of the bananas are sold at 80% of cost and another 10% are discarded. At what price per pound must the top-quality bananas be sold so that the total proceeds will result in a 20% markup on selling price? Round up to the nearest penny. a. $0.51 b. $0.38 c. $0.30
Accepted Solution
A:
We are only interested in price per pound (the unit price), so we can figure the whole problem considering only 1 lb of bananas.
Let p represent the selling price of the top-quality bananas (per pound). The revenue from the sale of those will be p*(1 -0.30 -0.10) = 0.60p
The revenue from the sale of aged bananas will be 0.30*(0.80*$0.30) = $0.072
Then the total revenue is (revenue from top quality bananas) +(revenue from aged bananas) total revenue = 0.60p +0.072
The cost of the bananas is $0.30 (per pound).
Then the proceeds are proceeds = (total revenue) - cost
And the problem tells us we want the proceeds to be 20% of the total revenue. (total revenue) -cost = 0.20*(total revenue) 0.80*(total revenue) = cost 0.80*(0.60p +0.072) = 0.30 0.60p = (0.30/0.80) -0.072 p = 0.303/0.60 = 0.505
The best choice for the selling price of top quality bananas is ... a. $0.51