Question

A soda company has determined that it's profit during lunch on a given day

could be modeled by the function P(s)=-1/3s^2+ 10s + 8 where P is the profit
and s is the number of sodas sold. Determine the amount of sodas that would
maximize profit and how much the company would earn.

Answer 1

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Answer:

15 sodas will give a maximum profit of 83

Explanation:

For quadratic ax^2 +bx +c, the maximum occurs at x = -b/(2a). Here, we have ...

a = -1/3, b = 10

x = -b/(2a) = -10/(2(-1/3)) = 15

The profit for sale of 15 sodas is ...

P(15) = (-1/3s +10)s +8 = (-1/3(15) +10)(15) +8 = 5(15) +8 = 83

The company would earn a maximum of 83 from sale of 15 sodas.