Question 1. The owner of a motel is considering outsourcing the daily room cleanup to Duffy's Maid Service. The manager rents an average of 50 rooms for each of 365 nights. The owner's cost to clean a room is $12. The Duffy's Maid Service quote is $18 per room plus a fixed cost of $24,000 for sundry items such as uniforms with the motel's room. The owner's fixed cost for space, equipment, and supplies is $60,000.

(a) Determine the crossover point for the two options. Please give the formula for calculating crossover points, at least one step of calculation, and the correct answer for full credit.

(b) Which option should be chosen and why?

Question 2. Historical demand for a product is

(a) Using a weighted moving average with weights of 0.6, 0.3, and 0.1. The weight of 0.6 is to be attached to the most recent demand and 0.3 to the second most recent demand. Compute the July forecast. For full credit, please provide at least one step of calculation and the correct forecast.

(b) Using a simple three-month moving average, compute the forecasts for April, May, and June. For each forecast, please provide at least one step of calculation and the correct value.

(c) Based on the forecasts from (b), Compute the mean absolute deviation (MAD) for the simple 3-month moving average method. For full credit, please provide the formula, at least one step of calculation, and the correct answer.

(d) Using exponential smoothing with α = 0.2 and a June forecast = 13, compute the forecast for July. For full credit, please provide the formula, at least one step of calculation and the correct forecast.

(e) Using simple linear regression analysis, calculate the regression equation for the product. For both parameters a and b, please provide the formula, at least one step of calculation, and the correct value for full credit.

(f) Using the regression equation from (d), calculate the forecast for July. Please provide one step of calculation and the correct answer for full credit.