Travis is a mid-level manager of a large retail chain. He works 60 hours a week and spends those hours primarily on two tasks: reviewing performance of different stores in the chain and studying market dynamics of various products sold by his chain. It takes him 4 hours to review a single store and 2 hours to properly study the market for a single product. The retail chain has thousands of stores and stocks over twenty thousand different products, so he never runs out of things to do.

Travis's utility from these activities is given by: u(S, P) = 10S^2/3 P^3/5

^{where S is the number of stores and P is the number of products he reviewed in a week.}

^{(a) Write down the budget line describing Travis's activities in a given week.}

^{(b) Find the marginal rate of substitution between stores and products.}

^{(c) Find demand: how many stores and products will Travis review per week?}

^{(d) High-level managers decided that store performance reviews are not detailed enough and came up with new standards for them. As a result, it now takes Travis 6 hours to nish a store report. How many store reports per week will he complete?}