Question

Profit The profit P (in dollars) made by a cinema from selling x bags of popcorn can be modeled by P = 2.32x - x^2/28,000 - 3,900, 0 ? x ? 50,000. (a) Find the intervals on which P is increasing and decreasing. (Enter your answers using interval notation.) increasing decreasing (b) If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain your reasoning. You should charge the price that yields sales of x = 31,980 bags of popcorn. Since the function changes from increasing to decreasing at x = 31,980, the minimum profit occurs at this value. You should charge the price that yields sales of x = 32,980 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,980, the maximum profit occurs at this value. You should charge the price that yields sales of x = 32,380 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,380, the minimum profit occurs at this value. You should charge the price that yields sales of x = 32,480 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,480, the maximum profit occurs at this value. You should charge the price that yields sales of x = 32,480 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,480, the minimum profit occurs at this value.

          Profit The profit P (in dollars) made by a cinema from selling x bags of popcorn can be modeled by
P = 2.32x - x^2/28,000 - 3,900, 0 ? x ? 50,000.
(a) Find the intervals on which P is increasing and decreasing. (Enter your answers using interval notation.)
increasing
decreasing
(b) If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain your reasoning.
You should charge the price that yields sales of x = 31,980 bags of popcorn. Since the function changes from increasing to decreasing at x = 31,980, the minimum profit occurs at this value.
You should charge the price that yields sales of x = 32,980 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,980, the maximum profit occurs at this value.
You should charge the price that yields sales of x = 32,380 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,380, the minimum profit occurs at this value.
You should charge the price that yields sales of x = 32,480 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,480, the maximum profit occurs at this value.
You should charge the price that yields sales of x = 32,480 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,480, the minimum profit occurs at this value.

Profit The profit P (in dollars) made by a cinema from selling x bags of popcorn can be modeled by
P = 2.32x - x^2/28,000 - 3,900, 0 ? x ? 50,000.
(a) Find the intervals on which P is increasing and decreasing. (Enter your answers using interval notation.)
increasing
decreasing
(b) If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain your reasoning.
You should charge the price that yields sales of x = 31,980 bags of popcorn. Since the function changes from increasing to decreasing at x = 31,980, the minimum profit occurs at this value.
You should charge the price that yields sales of x = 32,980 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,980, the maximum profit occurs at this value.
You should charge the price that yields sales of x = 32,380 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,380, the minimum profit occurs at this value.
You should charge the price that yields sales of x = 32,480 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,480, the maximum profit occurs at this value.
You should charge the price that yields sales of x = 32,480 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,480, the minimum profit occurs at this value.

Added by Cynthia F.

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