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Problem 5. (6 points) A bakery produces Cheesecakes using bakers (labor) and specialized baking ovens (capital). Let q be the number of cheesecake; produced per week, K be the number of hours of oven use, and L be the number of hours of labor use. The bakery's production function is given by q : 6K0.5L0.25_ The current hourly wage for bakers is a! = $20, and the per hour user cost of capital (ovens) is r = $10. (a) Derive the bakery's marginal rate of technical substitution of labor for capital (M RTSL, K). (2 points) (b) What is the optimal ratio of capital to labor at the cost-minimizing combination of inputs? {2 points) (c) How many labor hours (L) and oven hours (K) will the bakery use to minimize the cost of producing q = 300 Cheesecakes per week? Hint: You can allow for fractions of hours to be used. Keep any fractions up to 5 decimal places when making your caiwlations. (2 points)