SOLUTION: A grocery store is reevaluating the retail price of their oranges. They have a contract where they can purchase oranges for $0.52 per pound. However, this includes high quality ora

Question 1132695: A grocery store is reevaluating the retail price of their oranges. They have a contract where they can purchase oranges for $0.52 per pound. However, this includes high quality oranges (about 40% of the time), low quality oranges (55%), and occasionally rotten fruit (5%). Suppose they sell 80% of all high quality oranges at $1.99 per pound, 65% of all low quality oranges at $1.49 per pound (they offer a sale), and they cannot sell any of the rotten fruit.
What is the store's expected profit from a random shipment of 500 pounds of oranges? We do not consider personnel and other overhead costs, only the wholesale cost of the oranges. (Give your answer as a number, no dollar sign included.)
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

40% of the 500 pounds, or 200 pounds, is high quality; their profit per pound on those is $1.99-$0.52 = $1.47.
They sell 80% of those high quality oranges, which is 160 pounds. Presumably the other 20% of them (40 pounds) are not sold.

55% of the 500 pounds, or 275 pounds, is low quality; their profit per pound on those is $1.49-$0.52 = $0.97.
They sell 65% of those low quality oranges, which is 178.75 pounds. And again the assumption is the other 35% of those, 96.25 pounds, do not get sold.

So we have 160 pounds of oranges on which the profit per pound is $1.47 and 178.75 pounds on which the profit per pound is $0.97. The remaining oranges, 161.25 pounds, are not sold, at a "profit" per pound of -$0.52.

The expected profit on the 500 pounds is then

You can do the arithmetic.
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