need steps, explanation, and answer

Suppose that a firm's production function is q = 10L /2K/2. The cost of a unit of labor is $20 and the cost of a unit of capital is $80. a) What is the formula for your marginal rate of technical substitution for L with K (MRTSLK)? (Your answer should be a mathematical formula with the variables L and K in it.) b) If the firm receives a contract to produce 100 units of output, what is the cost-minimizing combination of inputs? C) Now imagine the firm wants to produce 140 units, but the amount of capital is now fixed at the level identified in (b). How many total units of labor will the firm need now?d) In the long run, once capital is a variable input, what will the cost-minimizing combination of inputs be (for producing 140 units)? e) Does this production function (q = 10L /