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Finite Mathematics

7th Edition
Stefan Waner + 1 other
ISBN: 9781337280426

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BuyFindarrow_forward

Finite Mathematics

7th Edition
Stefan Waner + 1 other
ISBN: 9781337280426
Textbook Problem

Income Because of the enormous success of the movie Henrietta’s Heaving Heart based on a novel by Celestine A. Lafleur (see Exercise 105), Boxoffice Success Produc­tions decides to film the sequel, Henrietta, Oh Henrietta. At this point, Bertha Snodgrass (whose novels now top the best-seller lists) feels that she is in a position to demand $100,000 for the screen rights and royalties of 8% of the net profits. Express her income I as a function of the net profit N, and determine the net profit necessary to bring her an income of $1,000,000. What is her marginal income (share of each dollar of net profit)?

To determine

To calculate: The linear model for the novelist, Celestine A. Lafleur’s income I as a function of the net profit N, her marginal income and also calculate the net profit in order to ear her an income of $1,000,000 when after the success of the movie Henrietta’s Heaving Heart based on her novel Ms. Lafleur decided to sold the screen rights of her book, Henrietta’s Heaving Heart to Box-office Success Productions at $100,000 and she gets royalties of 8% of the net profits additionally according to the contract.

Explanation

Given Information:

After the success of the movie Henrietta’s Heaving Heart based on her novel Ms. Lafleur decided to sold the screen rights of her book, Henrietta’s Heaving Heart to Box-office Success Productions at $100,000 and she gets royalties of 8% of the net profits additionally according to the contract.

Formula used:

The linear function or function is represented as y=mx+b, where m is the slope and b is the intercept.

The slope is computed when two points (x1,y1) and (x2,y2) are given as,

m=y2y1x2x1

And the intercept is computed for the line with slope m and passing through (x1,y1) as,

b=y1mx1

Calculation:

Consider that after the success of the movie Henrietta’s Heaving Heart based on her novel Ms. Lafleur decided to sold the screen rights of her book, Henrietta’s Heaving Heart to Box-office Success Productions at $100,000 and she gets royalties of 8% of the net profits additionally according to the contract.

Assume I be the income of Ms. Lafleur and N be the net profit.

As the income is the sum of the screen rights and the royalties taken, then the income is given by,

Income=Royalties+Screen Rights

Now, the screen rights is sold for $100,000 which means the value of screen rights is of 100,000 and the royalties is equal to 8% of the net profits which means the value of royalties is 0.08N.

Then, the equation for the income is as follows,

I=0

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