Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. Number NPrice p20053.0025052.5030052.0035051.50 (a) Find a formula for p in terms of N modeling the data in the table. p= (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month. R= Is R a linear function of N? (c) On the basis of the tables in this exercise and using cost, C=35N+900, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month. P= (d) Is P a linear function of N?

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Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.  Number NPrice p20053.0025052.5030052.0035051.50  (a) Find a formula for p in terms of N modeling the data in the table.  p=  (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month.  R=  Is R a linear function of N?  (c) On the basis of the tables in this exercise and using cost, C=35N+900, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month.  P=  (d) Is P a linear function of N?

Alannej · Accepted Answer

If there are more than three subparts, only the first three should be answered; if there are more, upload them separately.(a)&amp;nbsp;Consider the two points from table (a) as (200 53.00) and (250 52.50).&amp;nbsp;Then, the equation is,&amp;nbsp;p−p1=p2−p1N2−N1(N−N1)&amp;nbsp;p−53.00=52.50−53.00250−200(N−200)&amp;nbsp;p−53=−0.5050(N−200)&amp;nbsp;p−53=−0.01N+2&amp;nbsp;p=−0.01N+55&amp;nbsp;Thus, the equation&amp;nbsp;p=−0.01N+55&amp;nbsp;(b)&amp;nbsp;Think about the equation that relates the quantity N of widgets produced in a month to the manufacturer&#039;s total monthly revenue R, expressed in dollars.R=(−0.01N+55)N&amp;nbsp;=−0.01N2+55N&amp;nbsp;Thus, the formula is&amp;nbsp;R=−0.01N2+55N.&amp;nbsp;Here, R is not the linear function of N.&amp;nbsp;(c)&amp;nbsp;The formula for the monthly profit is,&amp;nbsp;P=−0.01N2+55N−35N−900&amp;nbsp;=−0.01N2+20N−900&amp;nbsp;Here, P is not the linear function of N.

Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be s

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