Chapter MPS, Problem 3.6MPS

a.

To determine

To find: The daily maximum income.

Answer to Problem 3.6MPS

The daily maximum income is $\$336$ .

Explanation of Solution

Given information: The prices for manicure and pedicure is $16 and $38.

Calculation:

Assume the manicure and pedicure is denoted by $x$ and $y$ respectively.

Consider the equation.

  $\begin{array}{l}\frac{20}{60}x+\frac{45}{60}y\le 7\\ \frac{1}{3}x+\frac{3}{4}y\le 7\end{array}$

Assume there is no more than 5 pedicures per day.

  $y\le 5$

The equation in terms of price is,

  $f\left(x,y\right)=16x+38y$

The graph is shown below.

  

Figure-1

Substitute the values in cost function.

  $\begin{array}{c}f\left(0,5\right)=16\left(0\right)+38\left(5\right)\\ =190\\ f\left(21,0\right)=16\left(21\right)+38\left(0\right)\\ =336\end{array}$

Thus, the daily maximum income is $\$336$ .

b.

To determine

To find: The daily maximum income with tip.

Answer to Problem 3.6MPS

The daily maximum income with tipis $\$378$ .

Explanation of Solution

Given information: The prices for manicure and pedicure is $16 and $38.

Calculation:

Assume the manicure and pedicure is denoted by $x$ and $y$ respectively.

Consider the equation.

  $\begin{array}{l}\frac{20}{60}x+\frac{45}{60}y\le 7\\ \frac{1}{3}x+\frac{3}{4}y\le 7\end{array}$

Assume there is no more than 5 pedicures per day.

  $y\le 5$

The equation in terms of price is,

  $f\left(x,y\right)=18x+45y$

The graph is shown below.

  

Figure-1

Substitute the values in cost function.

  $\begin{array}{c}f\left(0,5\right)=18\left(0\right)+45\left(5\right)\\ =225\\ f\left(21,0\right)=18\left(21\right)+45\left(0\right)\\ =378\end{array}$

Thus, the daily maximum income with tip is $\$378$ .