A paint manufacturing company has a manufacter function Q = K+ √L. For this manufacter function MPK = 1 and MPL = 1=(2√L). The rm faces a price of labor w that equivalent $1 per unit and a price of capital services r that equivalent $50 per unit.

a. Show that the rm's cost-minimizing input combination to produce Q = 10 involves no use of capital. (Hint: this is a corner solution.)

b. What must the price of capital down to in order for the rm to use a positive amount of capital, keeping Q at 10 and w at 1?

c. What must Q enhance to for the rm to use a positive amount of capital, keeping w at 1 and r at 50