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

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.

��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

100x + 200y <= 1400

0.6x + 0.8y <= 7.2
x/y >= 2/3

volume is .8x+1.2y

Now just follow the usual optimization steps.