Roberta runs a dress factory. She produces $50$ dresses per day, using labor and electricity. She uses a combination of labor and electricity that produces $50$ dresses per day in the cheapest possible way. She can hire as much labor as she wants at a cost of $20$ cents per minute. She can use as much electricity as she wants at a cost of $10$ cents per minute. Her production isoquants are smooth curves without kinks and she uses positive amounts of both inputs.

Question $6$ options:

a$)$

There is not enough information to determine the ratio of marginal products. We'd have to know the production function to know this.

b$)$

The marginal product of a minute of labor is equal to the marginal product of a kilowatt$-$hour of electricity.

c$)$

The marginal product of a kilowatt$-$hour of electricity is twice the marginal product of a minute of labor.

d$)$

The marginal product of a minute of labor plus the marginal product of a kilowatt$-$hour of labor must equal $50/(20+10).$

e$)$

The marginal product of a minute of labor is twice the marginal product of a kilowatt$-$hour of electricity.