A grocer sells 30 loaves of bread a day. The cost is $2.50 per loaf. The grocer estimates that for each $0.50 increase in cost, 2 fewer loaves of bread will be sold per day. Let x represent the number of $0.50 increases in the cost of a loaf of bread.

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Scott Perkins

Mathematics

28 June, 08:29

A grocer sells 30 loaves of bread a day. The cost is $2.50 per loaf. The grocer estimates that for each $0.50 increase in cost, 2 fewer loaves of bread will be sold per day. Let x represent the number of $0.50 increases in the cost of a loaf of bread.

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Lucian Ellison · Answer 1

If x is the number of $0.50 increases, then the cost of a loaf of bread will be (2.5 + 0.5x) then the number of loaves sold per day will be (30 - 2x).

Then the revenue will be the product of the cost and the number of loaves:

Revenue = (2.5 + 0.5x) (30 - 2x) = 75 + 10x - x^2

If we want to maximize revenue, we take its derivative and equate to 0:

d (Revenue) / dx = 10 - 2x = 0

x = 5

So to maximize revenue, x = 5, which corresponds to a price of (2.5 + 0.5x) = $5/loaf. This will correspond to sale of (30 - 2x) = 20 loaves. The total revenue will be ($5/loaf) * (20 loaves) = $100.