Question

A small rectangular warehouse is to be constructed which is to have an area of 10000 square feet. The building is to be partitioning internally in to eight equal parts. The costs have been estimated based on exterior and interior walls dimensions. The costs are $300 per running foot of exterior wall and plus $1100 per running foot of interior wall.   

Answer 1

question

a) Determine the dimensions which will minimize the construction costs?

b) What are the minimum costs?

solution

The area is 10000 sq.feet

Running cost for the exterior wall is $300

Running cost for interior wall is $1100

a) There are two dimensions will work out.

b)The one side of rectangle is represented as x, then becomes $\frac{10000}{x}$ . The smaller side is x and cost 1 can be denoted as,

$Cost=300(2x+\frac{2×10000}{x})+1100(3x+\frac{10000}{x})$

$Cost=600x+3300x+\frac{6000000}{x}+\frac{11000000}{x}$

$Cost=3900x+\frac{17000000}{x}$

The minimum value is $514975.728$ at $66.023.$

For cost 2,

$Cost=330(2x+\frac{2×10000}{x})+1100(7x)$

$Cost=8300x+\frac{6000000}{x}$

Answer:

a) The dimension to minimize the cost is $26.887×\frac{10000}{26.887}=26.887×371.97$

b) The minimum cost is 446318.272 $.