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kirill115 [55]
3 years ago
6

A community theater uses the function p(d)= -5d²+300d -200 to model the profit (in dollars) expected in a weekend when the ticke

ts to a comedy show are priced at d dollars each: Part A: Write and solve an equation to find out the prices at which the theater would earn $2,300 in profit from the comedy show each weekend. Show your reasoning Part B: At what price would the theater make the maximum profit. and what is that maximum profit? Show your reasoning.​
Mathematics
1 answer:
slava [35]3 years ago
6 0

Answer:

  • A. $66.33
  • B. $4300

Step-by-step explanation:

<u>Given function:</u>

  • p(d)= -5d² + 300d - 200
<h3>Part A</h3>

<u>p(d) = 2300, find d:</u>

  • 2300 = -5d² + 300d - 200
  • 5d² - 300d + 200 - 2300 = 0
  • 5d² - 300d - 2100 = 0
  • d² - 60d - 420 = 0
  • d²- 2*30d + 900 = 1320
  • (d - 30)² = 1320
  • d- 30 = √1320
  • d = 30 + 36.33
  • d = 66.33
<h3>Part B</h3>

<u>Maximum point of the function is obtained at vertex, which is (x = -b/2a):</u>

  • d = - 300/-10 = 30

<u>The maximum profit is:</u>

  • p(30) = -5(30)² + 300(30) - 200 = 4300
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