Please provide solution to the problem

1. Is Please show all your work in this question to receive full credit, and it must be neat enough to be clear. Consider Katie, whose firm uses two inputs, labor (L) and capital (K) to produce Katie's K9 dog treats. Let the production technology be given by Q =0.25KL The wage rate (w) is $12 per hour, and the rental rate on capital (r) is $22 per hour. She sells each bag for $5. Katie has landed a contract with Treats on a Leash in downtown SSM to supply 200 bags of Katie's K9 treats each month. She needs to decide how much labor and capital to employ in order to fulfill this contract. a . In the short run, capital is fixed at 8. What is the cost of producing 200 bags? b. at How much profit does she make (per month)? What should the firm do in the long run to minimize the cost of producing 200 bags? C. Find the cost minimizing combination of K and L. (Hint: You need to find MP, and MPx first to solve this problem) d. Show what this combination will cost and compare it to the short run cost. e. Is the profit from this contract in long run more or less than in the short run? f. Katie's K9 treats are wildly popular with SSM dogs. Treats on a Leash asks Katie if she could double her order to 400 bags per month. How much labor will Katie need to hire in the short run in order to fulfill the contract? (Hint: Use the production function to solve this