The Missing Link$$ Chain$-$Link Fence Company is trying to determine how many$$ chain$-$link fabricating machines to buy for its factory. If we define a$$ chain$-$link fence of some specified length to be equal to one unit of$$ output, the price of a new fabricating machine is $60$ units of$$ output, and the price of a$$ one$-$year$-$old machine is $51$ units of output. These relative prices are expected to be the same in the future. The expected future marginal product of fabricating$$ machines, measured in units of$$ output, is:

$MP{K}^f=165-0\mathrm{.}2K$

where $K$ is the number of machines in use. There are no taxes of any sort. The real interest rate is $6\%$ per year.

a$.$ What is the user cost of capital?

$($Enter your response rounded to one decimal place$).$

Specify the units in which your answer is measured.

b$.$ Determine the number of machines that will allow Missing Link to maximize its profit. machines $($Enter your response rounded to one decimal place$).$

c$.$ Suppose that Missing Link must pay a tax equal to $20\%$ of its gross revenue.

What is the optimal number of machines for the company? machines $($Enter your response rounded to one decimal place$).$

any new machines purchased.

place$).$