The cost in dollars to produce x cups of lemonade is represented by the function C (x) = 10 + 0.20x. The revenue in dollars earned by selling x cups of lemonade is represented by the function R (x) = 0.50x. What is the minimum number of whole cups of lemonade that must be sold for the revenue to exceed the cost?

Question

Mathematics

Jeffrey Jones

5 January, 05:13

The cost in dollars to produce x cups of lemonade is represented by the function C (x) = 10 + 0.20x. The revenue in dollars earned by selling x cups of lemonade is represented by the function R (x) = 0.50x. What is the minimum number of whole cups of lemonade that must be sold for the revenue to exceed the cost?

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Kyle Bond · Answer 1

For revenue to exceed cost: R (x) > C (x)

0.50x > 10 + 0.20x

0.50x - 0.20x > 10

0.30x > 10

x > 10/0.30

x > 33.333

Therefore the minimum number of whole cups of lemonade that must be sold for the revenue to exceed the cost is 34.