4 An air charter company has the following rules for selling seats on a flight.
- The total number of seats sold must not exceed 120.
- There must be at least 100 seats sold, or the flight will be cancelled.
- For every child seat sold there must be a seat sold for a supervising adult.
- Define two variables so that the three constraints can be formulated in terms of your variables. Formulate the three constraints in terms of your variables.
- Graph your three inequalities from part (i).
The price for a child seat is \(\pounds 50\) and the price for an adult seat is \(\pounds 100\). - Find the maximum income available from the flight, and mark and label the corresponding point on your graph.
- Find the minimum income available from a full plane, and mark and label the corresponding point on your graph.
- Find the minimum income available from the flight, and mark and label the corresponding point on your graph.
- At \(\pounds 100\) for an adult seat and \(\pounds 50\) for a child seat the company would prefer to sell 100 adult seats and no child seats rather than have a full plane with 60 adults and 60 children. What would be the minimum price for a child's seat for that not to be the case, given that the adult seat price remains at \(\pounds 100\) ?