Benefit for many manufacturing companies is often modeled by a parabolic functio

Question

Benefit for many manufacturing companies is often modeled by a parabolic function. there is a point at which the company will attain maximum profit by producing a specific mount of product. This is often determined through marketing and sales data. manufacturing company produces a profit that is defined by the following function: P(x) = -.2x^2 - 140x - 3375 where x represents the number of units sold. Based on this function, answer the following questions. Your answers should be clear and concise using proper mathematical terms. What profit does the company make if they sell 100 units? What is the maximum profit the company will make? How many units do they need to sell to achieve this maximum profit? What is the domain of the function based on the application? On graph paper, draw the graph of the function. Label the x-axis and y-axis and vertex according to the problem Does the graph open up or down? Why? Does this make sense in the context of the problem? Calculate the discriminate. Is the value for the discriminate what you expected? Why or why not? How many units does the company need to sell in order to make a minimum profit of 16, 625? If you would like to see this graph on your calculator, set your window to

Explanation / Answer

P(x) = -0.2x^2 + 140x - 3375

a) x = 100

P(100) = -0.2*100^2 + 140*100 - 3375 = 8625

b) , c) max. profit occurs at : x = -b/2a = - (140/2*-0.2) = 350 units sold

maxi. profit , P(350) = -0.2(350)^2 + 140*350 - 3375 = 21125

d) Domain : find x intercept P(x) =0 ; -0.2x^2 + 140x - 3375 =0

x =25 , 675

[ 25 , 675 ]

e) Since there is a maximum, graph would be facing downwards

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