Question

Prices to a concert cost N$ 200 for an adult and N$ 150 for a child, the convert venue can accommodate at most 240 people. The organizers are giving a N$ 20 discount to every adult and N$ 10 discount for every child but do not want the total discounted to exceed N$ 3200. Draw a graph and use it to answer the following questions. 1. How many tickets all together should the organizers sell in order to maximize their sales amount? 2. How many tickets of each type ( adult and child) should they sell to get a maximum sales amount? 3. What is the maximum sales amount the organizers can make? 4.If the profit is calculated as follows: profit = total sales - total discount amount. How much profit will the organizers from the maximum sales?

Answer 1

Let x be the number of adults, let y be the number of children

$$f(x,y)=200x+150y \rarr max$$

$$20x+10y\le 3200$$

$$x+y\le240$$

$$x\ge0, y\ge0$$

1. 200
2. Adults 80, children 160.
3. $f(80,160)=200\times80+150\times160=16000+24000=40000$
4. 40000-3200=36800