Chapter 3, Problem 38CP

a.

To determine

The number of tickets one must sell to start making profit.

Answer to Problem 38CP

In order to make profit, one must sell at least 39 tickets.

Explanation of Solution

Given:

The cost of DJ is given = $125.

The cost of Decorations is given = $47.50

The price of each ticket is given = $4.50

Concept Used:

The concept of forming and solving inequality is used.

Calculation:

Cost of DJ = $125

Cost of Decoration = $47.50

Total Cost Required = $125 + $47.50 = $172.50

Price of 1 ticket = $4.50

Let the number of tickets sold be $x$ .

The inequality to make profit becomes,

  $\Rightarrow 4.50x\ge 172.50$

Divide both sides with 4.50. The inequality becomes,

  $\Rightarrow x\ge 38.33$

Conclusion:

Thus, in order to make profit one must sell at least 39 tickets.

b.

To determine

The number of tickets, one must sell to get a profit of $300.

Answer to Problem 38CP

The annuity will run out of fund at $t=13.8629\text{years}$ .

Explanation of Solution

Given:

The cost of DJ is given = $125.

The cost of Decorations is given = $47.50

The price of each ticket is given = $4.50

The minimum profit is given = $300.

Concept Used:

The concept of forming and solving inequality is used.

Calculation:

Cost of DJ = $125

Cost of Decoration = $47.50

Total Cost Required = $125 + $47.50 = $172.50

Price of 1 ticket = $4.50

Minimum Profit = $300

Let the number of tickets sold be $x$ .

The inequality of profit becomes,

  $\Rightarrow 4.50x-172.50\ge 300$

Take 172.5 other side and add it in 300. The inequality becomes,

  $\Rightarrow 4.5x\ge 472.5$

Divide both sides by 4.5. The inequality becomes,

  $\Rightarrow x\ge 105$

Conclusion:

Thus, in order to get a profit of at least $300, one has to sell at least 105 tickets.

c.

To determine

The effect of raising the price of ticket to $5 on parts a and b

Answer to Problem 38CP

In order to make profit, one must sell at least 39 tickets.

Explanation of Solution

Given:

The cost of DJ is given = $125.

The cost of Decorations is given = $47.50

The price of each ticket is given = $5

Concept Used:

The concept of forming and solving inequality is used.

Calculation:

Effect on part a:

Cost of DJ = $125

Cost of Decoration = $47.50

Total Cost Required = $125 + $47.50 = $172.50

Price of 1 ticket = $5

Let the number of tickets sold be $x$ .

The inequality to make profit becomes,

  $\Rightarrow 5x\ge 172.50$

Divide both sides with 5. The inequality becomes,

  $\Rightarrow x\ge 34.5$

Effect on part b:

Minimum Profit = $300

Let the number of tickets sold be $x$ .

The inequality of profit becomes,

  $\Rightarrow 5x-172.50\ge 300$

Take 172.5 other side and add it in 300. The inequality becomes,

  $\Rightarrow 5x\ge 472.5$

Divide both sides by 5. The inequality becomes,

  $\Rightarrow x\ge 94.5$

Conclusion:

a) Thus, in part a, in order to make profit one must sell at least 35 tickets.

b) Thus, in order to make profit of at least $300 one must sell at least 95 tickets.