Roberta runs a dress factory. She needs to produces 80 dresses per day, using a combination of labor and sewing machine. She can hire as much labor as she wants at a cost of $10 per unit. She can rent as much sewing machine as she wants at a cost of $2.5 per unit. Her production function is y=5L1/2M1/2, where L is the amount of labor and M is the amount of machine. a. Write the equation for MRTS is:
MRTS=M/L 2M/L M1/2/L1/2 M/2L
(Hint: MPL=2.5L-1/2M1/2, MPM=2.5L1/2M-1/2
b. Find out Roberta’s demand for L and M, which can produce 100 dresses in the cheapest possible way.
c. Based on the solution from question b, calculate the lowest cost to product 100 dresses.
d. The local government raised the minimum wage from $10 to $22.5 per unit, ie the cost of labor is $22.5 now. With the new prices, calculate the lowest cost to produce 60 dresses.

Stocks a, b, and c are similar in some respects: each has an expected return of 10% and a standard deviation of 25%. stocks a and b have returns that are independent of one another; i.e., their correlation coefficient, r, equals zero. stocks a and c have returns that are negatively correlated with one another; i.e., r is less than 0. portfolio ab is a portfolio with half of its money invested in stock a and half in stock b. portfolio ac is a portfolio with half of its money invested in stock a and half invested in stock c. which of the following statements is correct? a. portfolio ab has a standard deviation that is greater than 25%.b. portfolio ac has an expected return that is less than 10%.c. portfolio ac has a standard deviation that is less than 25%.d. portfolio ab has a standard deviation that is equal to 25%.e. portfolio ac has an expected return that is greater than 25%.