Question

As part of its expansion plan, LA Se Storage is planning to construct a facility comprising storage units of sizes 10 ft × 10 ft, 10 ft × 15 ft, and 10 ft × 20 ft. The company has 13,500 ft² of floor spac available for the construction of 100 units. How many units of each size can the company con- struct if all the available floor space is utilized?

Answer 1

LA Se Storage can construct 135 units of size 10 ft × 10 ft, 90 units of size 10 ft × 15 ft, and 67 units of size 10 ft × 20 ft if all the available floor space is utilized.

Step-by-step explanation:

To determine how many units of each size LA Se Storage can construct, we need to calculate the total floor space required for each unit size and then divide the available floor space by the total space required for one unit of each size.

1. Calculate the total floor space required for one unit of each size:

1. For a 10 ft × 10 ft unit, the total floor space required is 10 ft × 10 ft = 100 ft².
2. For a 10 ft × 15 ft unit, the total floor space required is 10 ft × 15 ft = 150 ft².
3. For a 10 ft × 20 ft unit, the total floor space required is 10 ft × 20 ft = 200 ft².

2. Calculate the total floor space required for 100 units of each size:

1. For 100 units of size 10 ft × 10 ft, the total floor space required is 100 units × 100 ft² = 10,000 ft².
2. For 100 units of size 10 ft × 15 ft, the total floor space required is 100 units × 150 ft² = 15,000 ft².
3. For 100 units of size 10 ft × 20 ft, the total floor space required is 100 units × 200 ft² = 20,000 ft².

3. Divide the available floor space (13,500 ft²) by the total floor space required for one unit of each size to find out how many units of each size can be constructed:

1. For the 10 ft × 10 ft units, the company can construct 13,500 ft² / 100 ft² = 135 units.
2. For the 10 ft × 15 ft units, the company can construct 13,500 ft² / 150 ft² = 90 units.
3. For the 10 ft × 20 ft units, the company can construct 13,500 ft² / 200 ft² = 67.5 units. Since we cannot have a fraction of a unit, we can round down to the nearest whole number, so the company can construct 67 units.

Therefore, LA Se Storage can construct 135 units of size 10 ft × 10 ft, 90 units of size 10 ft × 15 ft, and 67 units of size 10 ft × 20 ft if all the available floor space is utilized.