Question

5! The office needs cabinets. The price for the first type of cabinet is $10, it

needs 6 ft2 of floor space, and it has a storage volume of 8 ft. The price
for the second type of cabinet is $20, it needs 8 ft? of floor space, and it
has a storage volume of 12 ft. The company wants to spend no more
than $140 and the office can hold up to 72 ft2 of cabinets. How can the
storage volume be maximized?​

Answer 1

The answer is below

Explanation:

Let x represent the number of 6 ft² to be purchased and y represent the number of 8ft² cabinet to e purchased.

x > 0 and y > 0

6 ft² cabinet cost $10 and 8 ft² cabinet cost $20, only $140 is available to spend, therefore the cost equation is:

10 x + 20 y ≤ 140

Also the office can hold only 72 ft², the space equation is:

6x + 8y ≤ 72

The volume equation is:

V = 8x + 12y

From the graph attached, we have to find the point with maximum volume by testing the point (12, 0), (0,7) , (8,3)

For (12, 0): V = 8(12) + 12(0) = 96 ft³

For (0, 7): V = 8(0) + 12(7) = 84 ft³

For (8, 3): V = 8(8) + 12(3) = 100 ft³

The (8,3) point has the maximum volume. That is 8 6 ft² cabinet and 3 8ft² cabinet