Please explain this question and show how you reached the final answer,

I have been having some difficulty grasping the concept, thank you!

Suppose a small, price-taking farmer uses water {W} and fertilizer {F} to produce pump kins (q). The amount of pumpkins this farmer can grow is given by the following production function: if = law +4F1\" The price of a water gallon is $5. The price of a unit of fertilizer is $2. The market price for a single pumpkin is $111]. (a) Compute the marginal products of both inputs. Show your work; otherwise you will not get full credit. [b] What is the main difference between the two marginal products you calculated in part {a}? {c} Show that the cost-minimizing amount of fertilizer is U4. Hint: use TRSi-Jw. [d] Now, assume that, in the short-run, the farmer has a xed amount of EU gallons of water. However, she can hu}:r anyr amount of fertilizer she wants. Given this scenario, show that this farmer's short-run marginal cost function {SMC} is q {4 12.5. (e) Recall that the rm is a price-taker. What is the prot-maximizing output the farmer will produce