(a)

Let be the number of pounds of the commodity costing per pound. Because there are pounds total, the amount of the second commodity is .

The total cost is .

.

(b)

Find the inverse of the original function.

Interchange the variables  and .

Substitute .

The inverse of the function is .

In the inverse function , represents total cost and represents number of pounds of the less expensive commodity.

(c) Domain of inverse function:

The total cost will be minimum if we buy pounds of less expensive commodity.

Therefore, the minimum value of is

The total cost will be maximum if we buy pounds of more expensive commodity.

Therefore, maximum value of is .

Domain of inverse function is .

(d)

Number of pounds of less expensive commodity is when .

.

(a) .

(b) The inverse function , where represents total cost and represents number of pounds of the less expensive commodity.

(c) Domain of inverse function is .

(d) .