I need to find whether or not the company is making an optimal inout choice.

largo publishing house uses 400 printers and 200 printers to produce books. A printers wage is 20. and the price of a printing press is 5000. the last printer added 20 books to total output while the last press added 1000 books.
am i on the right track
k=c/r-w/r*l or do i use the
c= wl+rk

The firm makes an optimal input choice when the marginal product of one input divided by the price (wage) is equal the marginal product of any other input divided by the price (wage) of that other input.

So for printers MP=20, P=20. So MP/P=1

For presses, MP=1000, P=5000. So, MP/P=0.2

The firm should hire more printers and use less presses.

To determine whether or not the company is making an optimal input choice, we can use the concept of marginal productivity and cost.

The formula you mentioned, k=c/r-w/r*l, is an equation for calculating the marginal cost of labor. In this equation:
- k represents the marginal cost of labor.
- c represents the total cost.
- r represents the marginal productivity of labor.
- w represents the wage rate.
- l represents the quantity of labor.

The formula you mentioned, c= wl+rk, is an equation for calculating the total cost. In this equation:
- c represents the total cost.
- w represents the wage rate.
- l represents the quantity of labor.
- r represents the rental cost of capital.
- k represents the quantity of capital.

To determine if the company is making an optimal input choice, we need to compare the marginal productivity of labor and capital with their respective costs.

First, we need to calculate the marginal productivity of labor and capital. The marginal productivity of labor is the additional output gained from adding one more unit of labor, while the marginal productivity of capital is the additional output gained from adding one more unit of capital.

In this case, the last printer added 20 books to the total output, so the marginal productivity of labor is 20 books. And the last press added 1000 books, so the marginal productivity of capital is 1000 books.

Next, we compare the marginal productivity with their respective costs. The wage rate for a printer is $20, and the rental cost of a printing press is $5000.

If the marginal productivity divided by the cost is greater for labor compared to capital, then it suggests that the company should hire more labor. Similarly, if the marginal productivity divided by the cost is greater for capital compared to labor, then it suggests that the company should invest more in capital.

For example, if the marginal productivity of labor per dollar spent on labor is higher than the marginal productivity of capital per dollar spent on a printing press, it would indicate that hiring more printers would be a more optimal choice.

By calculating and comparing these values, you can determine whether the company is making an optimal input choice.