Chapter 2.5, Problem 81AYU

(a)

To determine

To sketch: the graph of $Y_1=p\left(x\right)-10000$ and $Y_2=\left(1-0.10\right)p\left(x\right)$ .

Explanation of Solution

Given information:

The daily profits of cigar company from selling $x$ cigars are given by

  $p\left(x\right)=-0.05x^2+100x-2000$

The company the option of either paying a flat tax of $10000 per day or a tax of 10% on profits

Calculation:

The graphs of $Y_1=p\left(x\right)-10000$ and $Y_2=\left(1-0.10\right)p\left(x\right)$ are as follows

  

(b)

To determine

To find: the better option based on the graph.

Answer to Problem 81AYU

One should select option number 2, because that will make more profit than that of option 1.

Explanation of Solution

Given information:

The daily profits of cigar company from selling $x$ cigars are given by

  $p\left(x\right)=-0.05x^2+100x-2000$

The company the option of either paying a flat tax of $10000 per day or a tax of 10% on profits

Calculation:

I would select option number 2, because that will make more profit than that of option 1.

(c)

To determine

To describe: given graph in terms of the graph of $p\left(x\right)$ .

Explanation of Solution

Given information:

The daily profits of cigar company from selling $x$ cigars are given by

  $p\left(x\right)=-0.05x^2+100x-2000$

The company the option of either paying a flat tax of $10000 per day or a tax of 10% on profits

Calculation:

The graph $Y_1=p\left(x\right)-10000$ is obtained by shifting graph of $p\left(x\right)$ downwards by 10000 cigars.

And the graph of $Y_2=\left(1-0.10\right)p\left(x\right)$ is obtained by compressing the graph of $p\left(x\right)$ multiplying it with 0.9.

(d)

To determine

To find: the better option to select.

Answer to Problem 81AYU

Then I would choose any of the option because they fetch almost the same profit.

Explanation of Solution

Given information:

The daily profits of cigar company from selling $x$ cigars are given by

  $p\left(x\right)=-0.05x^2+100x-2000$

The company the option of either paying a flat tax of $10000 per day or a tax of 10% on profits

Suppose that the government offered the options of a flat tax of $4800 or a tax of 10%on profits.

Calculation:

The graphs then would be

  

Then I would choose any of the option because they fetch almost the same profit.