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Lucy’s Perfect Pizza sells every pizza for $12. Lucy currently has 400 customers per day.
She is considering raising the price for each pizza in order to maximize her daily income.
She estimates that the business will lose 10 customers per day for every $0.50 in the price of the pizza.
Write a function to represent Lucy’s daily income as a function of the number of $0.50 increases in the price of pizza.
Determine the x- and y-intercepts and explain what each represents in the context of the problem situation.
Determine the maximum daily income for Lucy’s Perfect Pizza, the corresponding pizza price,
and the corresponding number of daily customers. Thank you!
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The price of the pizza after n increases of the price
p = 12 + 0.5*n dollars.
The number of the customers after n increases of the price
N = 400 - 10n.
The income (the revenue function)
R = p*N = (12 + 0.5n)*(400-10n).
X-intercepts are n = = 40 and n = = -24.
Optimal number of increases is exactly half-way between the x-intercepts
= = = 8.
Optimal number of customers
= 400 - 10*8 = 400 - 80 = 320.
Optimal price
= 12 + 0.5*8 = 16.
Maximum daily income
= = 320*16 = 5120 dollars.
Solved.