Minimum Cost $\$ 6$ Per Foot and the Fence for the Middle Costs

question 39

Multiple Choice

Minimum cost. From a tract of land, a developer plans to fence a rectangular region and then divide it into two identical rectangular lots by putting a fence down the middle. Suppose that the fence for the outside boundary costs $\$ 6$ per foot and the fence for the middle costs $\$ 4$ per foot. If each lot contains $2200$ square feet, find the dimensions of each lot that yield the minimum cost for the fence.

• A)Dimensions are 61.86 ft for the side parallel to the divider and 35.56 ft for the other side.
• B)Dimensions are 35.56 ft for the side parallel to the divider and 61.86 ft for the other side.
• C)Dimensions are 46.90 ft for the side parallel to the divider and 46.90 ft for the other side.
• D)Dimensions are 40.62 ft for the side parallel to the divider and 54.16 ft for the other side.
• E)Dimensions are 54.16 ft for the side parallel to the divider and 40.62 ft for the other side.

---

Definitions:

Payback Period

The time it takes for an investment to generate an amount of income or cash equal to the cost of the investment, used to assess the profitability or risk of an investment.

Net Present Value

A financial metric that calculates the value of a series of cash flows by discounting them to the present value using a specific rate, often used to assess the profitability of an investment.

Net Present Value

The difference between the present value of cash inflows and outflows over a period, used to analyze the profitability of an investment.

Projected Annual Cash Inflow

An estimate of the total money expected to be received by a company over a year from its operational activities.