[4 points] A plant's production function is Q=LK , where MP1. = K and MPK = L. The price of Labour is $4 and t he price of capital is $2. a. If the rm has its capital xed at K=10, nd the amount of labour it must hire to produce 50 units. b. If the fact that K is xed at 10, more costly for the rm? By how much? [4 points] Suppose that the production function is C1=10K+5L and that MPL = 5 and MPK = 10. The price of Labour is $3 and t he price of capital is $2. 3. Find the optimal input choice (L and K) if the rm wanted to produce 50 goods. b. c. Plot the expansion path on the diagram in b). d. Find the input demand function of l. and K. (without knowing prices of Q, I want the general case) [2 points] for a given quantityr of output, under which condition would the short run quantity demanded of inputs be equal to the long run quantity of inputs demanded