TYPE FEES PER PUPIL FULL TIME PUPIL PART TIME PUPUL $200 $100 The table above shows the cost of tuition per week for a private school. The conditions under which the school operates are as follows: 1. The maximum number of places at the school in 75. 2. There must be a minimum of 20 full time pupils 3. The number of part time pupils must be at least half the number of full time pupils. 4. The minimum weekly income must be $6000. I. Formulate a linear programming model for this situation. II. Represent this model on a graph using a scale of 1 cm to 5 units on each axis. III. Find the numbers of full time and part time pupils that will maximise the profit if $40 profit is made on each full time student and $30 on each part-time student. IV. State the maximum profit.
| TYPE | FEES PER PUPIL |
|
FULL TIME PUPIL PART TIME PUPUL |
$200 $100 |
The table above shows the cost of tuition per week for a private school. The conditions under which the school operates are as follows:
1. The maximum number of places at the school in 75.
2. There must be a minimum of 20 full time pupils
3. The number of part time pupils must be at least half the number of full time pupils.
4. The minimum weekly income must be $6000.
I. Formulate a linear programming model for this situation.
II. Represent this model on a graph using a scale of 1 cm to 5 units on each axis.
III. Find the numbers of full time and part time pupils that will maximise the profit if $40 profit is made on each full time student and $30 on each part-time student.
IV. State the maximum profit.
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