I'm struggling with this practice question

1. A certain firm produces output (X) with machine hours of capital (K) and with hours of labor (L). Its production function' 15 given by X=1/2VKL 1. Fill in the following table with all the integer values of machine hours and labor hours that generate 2, 3, 4, 5 and 6 units of output. Those input combinations that generate 1 unit of output have been lled in below. K=1 ,L=4 ; K=2 , L=2 ; K=4 L=1 2. Plot the factor combinations um Table 1 on a graph (gure 1) with units of labor on the X axis and units of capital on the Y axis. (You may leave out the extreme input combinations that generate output levels of 5 and 6 units, e.g. 144K, 11..) 3. Solve for the marginal rate of technical substitution. 4. [fa machine can be rented for $24 per heur and a laborer can be hired for $6 per hour, solve for the best (i. e. the most inexpensive) combinations of K and L for producing our 1 to 6 units of output. Sketch the solution in gure 1. 5. Use your results to compute the long run total cost, average total cost and marginal cost curves. 6. Suppose that our rm has already rented four units of capital and can obtain no more over the next production period. Solve for the short run total cost, short run average cost and short run ' marginal cost curves