Aaron own a shipping company. He plans to move into his new office which is near to the city centre. He needs some filing cabinets to organize his files. Cabinet x which costs RM100 per unit, requires 0.6 square meters of the floor space and can hold 0.8 cubic meters of files. Cabinet y which costs RM200 per unit, requires 0.8 square meters of the floor space and can hold 1.2 cubic meters of files. The ratio of the number of cabinet x to the number of cabinet y is not less than 2:3. Aaron has an allocation of RM1400 for the cabinets and the office has room for no more than 7.2 square meters.

Question

��i) Using the given information,�
a) write the inequalities which satisfy all the above constraints,�
b)construct and shade the region that satisfies all the above constraints.
�ii)Using two different methods, fin the maximum storage volume
�iii) Aaron plans to buy cabinet x in a range of 4 to 9 units. Tabulate all the possible combinations of the cabinets that he can purchase. Calculate the cost of each combination.�
iv) If you were Aaron which combination would you choose? Justify your answer and give your reasons.

Answer 1

It is an optimization problem.

Here are some steps to solve the problem:
1. define variables (values that are to be found).
2. Reread the question, and translate each constraint into an inequality.
3. Graph the constraints and select the feasible region, using the variables as the axes.
4. Determine the coordinates of the vertices of the feasible region.
5. tabulate the storage volume for each point, and select the vertex having the maximum storage volume. Remember that the variables (number of filing cabinets) must be integers.
6. In (iv), you have to add additional constraints and then repeat steps 4 and 5.

Show how far you have gone with these steps and post if you encounter difficulties.