Linda loves buying shoes and going out to dance. Her utility function for pairs of shoes, S, and the number of times she goes dancing per month, T, is U(S,T)=5ST. It costs Linda $50 to buy a new pair of shoes, and $25 to spend an evening dancing.

a. Identify three bundles that provide a utility of 100.

b. Assume that she has $400 to spend on clothing and dancing. Find Linda's utility maximizing bundle of S and T.

c. Assume that the price of shoes increases to $100 and her nominal income remains at $400. Find Linda's utility maximizing bundle of S and T.

d. Based on your response to (b) and (c), derive the equation for Linda's linear inverse demand curve for shoes (i.e., if we assume a linear function al form for Linda's demand function, e.g., Ps = mS + C, calculate the intercept (C) and slope (m) parameters.