Amanda owns a toy manufacturing plant with the production function Q = 100L - 3000, where L is hired labor hours. Assume that Amanda has no fixed costs.
a. Rearrange Amanda's production function to show how many workers Amanda would have to hire to produce a given level of output. In other words, isolate L on the left-hand side, expressing L as a function of q.
b. Because Amanda has no fixed costs, all her costs come from paying workers. In other words, TC = w * L. Substitute your answer from (a) into this equation to find Amanda's total cost function.