Cabinet x which $100 per unit,requires 0.6 square meters of the floor space and can hold 0.8 cubic meters of files.Cabinet y which costs $200 per unit, requires 0.8 square meters of the floor space and can hold 1.2 cubic meters of files. the ratio the number of cabinet x to the number of cabinet y is not less than 2:3. aaron has an allocation of $1400 for the cabinets and the office has room for no more than 7.2 square meters.

Question

Cabinet x which $100 per unit,requires 0.6 square meters of the floor space and can hold 0.8 cubic meters of files.Cabinet y which costs $200 per unit, requires 0.8 square meters of the floor space and can hold 1.2 cubic meters of files. the ratio the number of cabinet x to the number of cabinet y is not less than 2:3. aaron has an allocation of $1400 for the cabinets and the office has room for no more than 7.2 square meters.

Answer 1

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Answer 2

To solve this problem, we need to find out how many units of each cabinet can be purchased within Aaron's budget and the space constraints of the office. Let's break down the steps:

1. Define the variables:
- Let's assume the number of cabinets of type X as 'x', and the number of cabinets of type Y as 'y'.

2. Determine the cost constraint:
- The cost of each cabinet X is $100, and the cost of each cabinet Y is $200.
- The total cost of cabinet X is 100x, and the total cost of cabinet Y is 200y.
- According to the problem, Aaron's budget is $1400, so the cost constraint is: 100x + 200y ≤ 1400.

3. Determine the space constraint:
- Cabinet X requires 0.6 square meters per unit, and cabinet Y requires 0.8 square meters per unit.
- The total space occupied by cabinet X is 0.6x, and the total space occupied by cabinet Y is 0.8y.
- According to the problem, the office has a space constraint of no more than 7.2 square meters, so the space constraint is: 0.6x + 0.8y ≤ 7.2.

4. Determine the ratio constraint:
- The ratio of X to Y should be 2:3 or greater, which means x/y ≥ 2/3.

5. Solve the problem:
- Now, we need to find the values of 'x' and 'y' that satisfy all the constraints mentioned above.
- This can be done by using techniques such as linear programming or by graphing the constraints and finding the feasible region.
- Once we obtain the feasible region, we can find the values of 'x' and 'y' that maximize the objective function (in this case, the number of cabinets).
- Keep in mind that 'x' and 'y' must be whole numbers since they represent the number of cabinets.

By following these steps, you should be able to find the optimal values of 'x' and 'y' that maximize the number of cabinets within Aaron's budget and the space constraints of the office.