Chapter ISG, Problem 9.9.2.3P

a.

To determine

To find a function to represent price of granola bags and total number of bags sell.

Answer to Problem 9.9.2.3P

Function of price

  $P(x)=4+0.25x$

Function of sell

  $S(x)=185-10x$

Explanation of Solution

Given information:

Price of one bag is $4

Number of bag sell is 185 Let x be the increase of $0.25 in the price of a bag

S sell 10 fewer bags

Calculation:

Price of one bag $=4$

Number of bag sell $=185$

Let x be the increase of $\$0.25$ in the price of a bag

S sell 10 fewer bags

Then

Function of price

  $P(x)=4+0.25x$

Function of sell

  $S(x)=185-10x$

b.

To determine

To find the revenue of the bags.

Answer to Problem 9.9.2.3P

  $R(x)=740+6.25x-2.5x^2$

Explanation of Solution

Given information:

Function of price

  $P(x)=4+0.25x$

Function of sell number of bag sell

  $S(x)=185-10x$

Calculation:

Function of price

  $P(x)=4+0.25x$

Function of sell number of bag sell

  $S(x)=185-10x$

Revenue

  $R(x)=(4+0.25x)(185-10x)$

On solving,

  $R(x)=740+46.25x-40x-2.5x^2$

On solving,

  $R(x)=740+6.25x-2.5x^2$

c.

To determine

To find revenue of bags when price of bag $\$4.75$ .

Answer to Problem 9.9.2.3P

Not good idea

Explanation of Solution

Given information:

  $R(x)=740+6.25x-2.5x^2$

Calculation:

Initial price in $ $=4$

New price in $ $=4.75$

Let x be the number of $\$0.25$ increase

Here

  $x=3$

Function of revenue

  $R(x)=740+6.25x-2.5x^2$

Put $x=3$

  $R(3)=740+6.25(3)-2.5{(3)}^2$

On solving,

  $R(3)=740+18.75-22.5$

On solving,

  $R(3)=736.25$

For $0.75 increase in price of bag

A can sell 30 fewer bags

So, this is not good idea