Please give a thorough explanation with steps. thank you!

Suppose that the rm uses three inputs to produce its output: capital K, labor L, and materials M. The rm's production function is given by Q = KiLiM i - For this production function, the marginal products of capital, labor, and materials are MPK= K_3L3M3, MPL 3K 3L 3M3, and MPH: 3[(313114 .The prices of capital labor, and materials are r = 1, w = 1, and m- 1, respectively. (a) What is the solution to the rm's long-run cost minimization problem given that the rm wants to produce Q units of output? (b) What is the solution to the rm's short-run cost- minimization problem when the rm _wants to produce Q units of output and capital is xed at K ? (c) When Q = 4, the long-run cost-minimizing quantity of capital is 4. If capital is xed at I? = 4 in the short run, show that the shortrun and long-run cost-minimizing quantities of labor and materials are the same