In 2009, the board of regents responsible for all public higher education funding in a large Midwestern state hired a consultant to develop a series of enrollment forecasting models, one for each college. These models used historical data and exponential smoothing to forecast the following year’s enrollments. Based on the model, which included a smoothing constant (α) for each school, each college’s budget was set by the board. The head of the board personally selected each smoothing constant based on what she called her "gut reactions and political acumen." What do you think the advantages and disadvantages of this system are? Answer from the perspective of (a) the board of regents and (b) the president of each college. How can this model be abused and what can be done to remove any biases? How can a regression model be used to produce results that favor one forecast over another?

The monthly demand equation for an electric utility company is estimated to be p equals 60 minus left parenthesis 10 superscript negative 5 baseline right parenthesis x, where p is measured in dollars and x is measured in thousands of killowatt-hours. the utility has fixed costs of $3 comma 000 comma 000 per month and variable costs of $32 per 1000 kilowatt-hours of electricity generated, so the cost function is upper c left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 32 x. (a) find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) suppose that the rising fuel costs increase the utility's variable costs from $32 to $38, so its new cost function is upper c 1 left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 38 x. should the utility pass all this increase of $6 per thousand kilowatt-hours on to the consumers?