statistics, management sciecne

662 Test 1 (Clearly place your answer under each question. Attach the Excel file you use to find the solution as a supporting document if you desire.)

1. The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, a) How many pounds of each seed should be in the blend? b) Which targets will be exceeded? c) How much will the blend cost?

	Type A	Type B
Shade Tolerance	1	1
Traffic Resistance	2	1
Drought Resistance	2	5

2. Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing. The profit per roll of Grade X carpet is $200 and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use.

a) Develop a linear programming model for this problem.

b) Solve the linear model for optimal solutions

c) Interpret the utilization of resources.

3. Sales (in thousands) of the new Thorton Model 506 convection oven over the eight-week period since its introduction have been as follows:

Week	Sales
1	18.6
2	21.4
3	25.2
4	22.4
5	24.6
6	19.2
7	21.7
8	23.8

a) Use Naïve forecast, compute the accuracy measures and what is the forecast for week 9?

b) Use average of past values forecast, compute the accuracy measures and what is the forecast for week 9?

c) Use three week moving average, compute the accuracy measures and what is the forecast for week 9?

d) Use three week weighted moving average with weights of 0.2, 0.3 and 0.5, compute the accuracy measures and what is the forecast for week 9?

e) Compare the forecast methods used in a though d, which method should be used?

f) Which exponential smoothing model provides better forecasts, one using  = .6 or  = .2? Compare them using mean squared error. What are the forecasts for week 9?

4. A 24-hour coffee/donut shop makes donuts every eight hours. The manager must forecast donut demand so that the bakers have the fresh ingredients they need. Listed below is the actual number of glazed donuts (in dozens) sold in each of the preceding 13 eight-hour shifts.

Date	Shift	Demand(dozens)
June 3	Day	59
	Evening	47
	Night	40
June 4	Day	64
	Evening	43
	Night	39
June 5	Day	62
	Evening	46
	Night	42
June 6	Day	60
	Evening	45
	Night	40
June 7	Day	58

a. Produce a line chart

b. Develop the optimization model that finds the estimated regression equation that minimize the sum of squared error.

c. Solve for the estimated regression equation.

d. Forecast the demand for glazed donuts for the Day, Evening, and Night shifts of June 8.

5. Design a scenario that requires to conduct a multiple regression analysis. You need to find data, construct the linear model, run analysis, evaluate your model, and interpret the results.