Jim works at a chocolate factory. One of Jims' employment perks is consumption of an unlimited number of chocolate bars for free.

Jim works at a chocolate factory. One of Jims’ employment perks is consumption of an unlimited number of chocolate bars for free. Jims’ weight is increasing both in the number of chocolate bars and in the calorie content of each chocolate bar. The only thing that keeps Jim from eating chocolate bars all the time is the effect that chocolate consumption has on his body weight. Jims’ preferences can be represented by the utility functionU (W, C) = 50 * square root (C) – W,where W denotes Jim’s weight and C denotes the number of chocolate bars consumed daily by Jim. Jim’s weight is given by the formulaW = 170 + aC/10,where a denotes the number of calories in each chocolate bar and C is the number of chocolate bars eaten daily by Jim. Furthermore, suppose that initially a = 100.a) Solve for Jim’s optimal chocolate bar consumption and weight.(Hint. Substitute the formula for Jim’s weight into the utility function so that the utility function becomes a function of one variable. Then find the value of C that maximizes Jim’s utility by taking advantage of the relationship between the maximum of a function and it’s derivative).

Jim works at a chocolate factory. One of Jims’ employment perks is consumption of anunlimited number of chocolate bars for free. Jims’ weight is increasing both in thenumber of chocolate bars...