You manage a firm in Minneapolis that produces bikes. Previously all production took place in Plant 1 that was built in 1960. The firm has recently invested in Plant 2 which uses newer technology. The cost curves for the plants are: for Plant 1 c₁(q) = 25 + 8q + 5q² and for Plant 2 c₂(q) = 100 + 4q + 3q² where all the costs are avoidable and the units are in terms of 100s of bikes. The firm has three options of supplying output: only Plant 1, only Plant 2 or Optimally Split Between both plants. Based on this information answer the following questions. a) Suppose the quantity of bikes to be produced is q=14. How will you manage the production. Mention if either one or both of the plants are used. Mention the final cost and amount produced in each plant. b) Now consider the problem of producing q=5 bikes. i) Show that the best option is to produce all the bikes in Plant 1. ii) Compute the marginal costs for the last bike produced. If it is in Plant 1 it will be the fifth bike produced in Plant 1. If it is produced in Plant 2 it is the first bike produced in Plant 2. Calculate the marginal cost of the fifth bike at Plant 1, i.e. MC₁(5). Calculate the marginal cost of the first bike at Plant 2, i.e. MC₂(1). Which plant has the lowest marginal cost of production?