Chapter MPS, Problem 3.8MPS

To determine

To Find: The number of car and bus that attendant accept to maximize the income

Answer to Problem 3.8MPS

  $\begin{array}{l}\text{→}\text{Number of car}=50\\ \text{→}\text{Number of bus}=10\end{array}$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Parking lot area}=600\text{ square meters}\\ \text{Space occupied by car}=6\text{ square meters}\\ \text{Space occupied by bus}=30\text{ square meters}\\ \text{Total vechile attendant can handle}=60\\ \text{Charge of parking one car}=\$3\\ \text{Charge of parking one bus}=\$8\end{array}$

Formula Used:

  $\begin{array}{l}\text{→}\text{Total number of car}\left(\text{Parking area of one car}\right)+\text{Total number of bus}\left(\text{Parking area of one bus}\right)=\text{Total parking lot area}\\ \text{→}\text{Total payment collected}=\text{Payment collected from car parking}+\text{Payment collected from bus parking}\end{array}$

Calculation:

  $\begin{array}{l}\text{Total number of vechile}=60\\ \text{Let the number of car}=60-x\\ \text{Number of bus}=x\\ \text{→}\text{Total number of car}\left(\text{Parking area of one car}\right)+\text{Total number of bus}\left(\text{Parking area of one bus}\right)=\text{Total parking lot area}\\ \text{⇒}\left(60-x\right)\left(6\right)+x\left(30\right)=600\\ \text{⇒}360-6x+30x=600\\ \text{⇒}360+24x-360=600-360\left(\text{subtract both side by 360}\right)\\ \text{⇒}24x=240\\ \text{⇒}\frac{24x}{24}=\frac{240}{24}\left(\text{Divide both side by 24}\right)\\ \text{⇒}x=10\\ \text{→}\text{number of car}=60-x=60-10=50\\ \text{→}\text{Number of car}=50\\ \text{→}\text{Number of bus}=10\\ \text{→}\text{Total payment collected}=\text{Payment collected from car parking}+\text{Payment collected from bus parking}\\ \text{⇒}\text{Total payment collected}=50\left(\$3\right)+10\left(\$8\right)\\ \text{⇒}\text{Total payment collected}=\$150+\$80\\ \text{⇒}\text{Total payment collected}=\$230\end{array}$

Conclusion:

Total number of bus and car that attendant accept to maximize the income is

  $10\text{ Bus and }50\text{ Car}$