Chapter 7.4, Problem 31E

a.

To determine

To calculate: how much money must be spent on an artwork if the project is expected to cost $30,000,000.

Answer to Problem 31E

The amount that must be spent on an artwork is $250,000.

Explanation of Solution

Given information: in New York’s percent of Art Programs, money is set aside for creating artwork at public building sites. The program requires that 1% of the first $20,000,000 of the cost of a building project and 0.5% of the remaining cost be spent on artwork.

Calculation:

It is provided that the expected cost of the artwork is $30,000,000

Calculate the cost of building project,

  $\begin{array}{l}1\%·\$20,000,000=\frac{1}{100}·\$20,000,000\\ =200,000\end{array}$

With the first $20,000,000, 1% is set aside for cost of building a project, then the remaining cost is,

  $\$30,000,000-\$20,000,000=\$10,000,000$

The amount to be spent on the artwork from the remaining cost,

  $\begin{array}{l}0.5\%·10,000,000=\frac{0.5}{100}·10,000,000\\ =50,000\end{array}$

The amount that must be spent,

  $\$200,000+\$50,000=\$250,000$

Hence, the amount that must be spent on an artwork is $250,000.

b.

To determine

To calculate: the percent of the yearly maximum amount is used by the two projects.

Answer to Problem 31E

50.66% of the maximum amount has been spent on artwork for the two projects in 1 year.

Explanation of Solution

Given information: for each project, no more than $400,000 can be spent on artwork. The maximum amount that can be spent on artwork per year on projects in the city is $1,500,000. Suppose that in one year the city has a project that costs $50,000,000 and another project that costs $62,000,000.

For project that costs $50,000,000,

Calculate the cost of building project,

  $\begin{array}{l}1\%·20,000,000=\frac{1}{100}·20,000,000\\ =200,000\end{array}$

The remaining money after setting aside 1% of the first $20,000,000 is,

  $\$50,000,000-\$20,000,000=\$30,000,000$

The money spent on artwork from the remaining cost,

  $\begin{array}{l}0.5\%·30,000,000=\frac{0.5}{100}·30,000,000\\ =\$150,000\end{array}$

Amount that must be spent on the artwork,

  $\$200,000-\$150,000=\$350,000$

For project that costs $62,000,000,

Calculate the cost of building project,

  $\begin{array}{l}1\%·20,000,000=\frac{1}{100}·20,000,000\\ =200,000\end{array}$

The remaining money after setting aside 1% of the first $20,000,000 is,

  $\$62,000,000-\$20,000,000=\$42,000,000$

The money spent on artwork from the remaining cost,

  $\begin{array}{l}0.5\%·42,000,000=\frac{0.5}{100}·42,000,000\\ =\$210,000\end{array}$

Amount that must be spent on the artwork,

  $\$200,000-\$210,000=\$410,000$

The total money spent on the artwork in the two projects is,

  $\$410,000+\$350,000=\$760,000$

Percent of maximum amount spent per year,

  $\frac{760,000}{1,500,000}\times 100=50.66\%$

Hence, 50.66% of the maximum amount has been spent on artwork for the two projects in 1 year.