Decision Analysis
Unidyde is considering expansion of its Fort Myers plant to produce a new chemical compound. The company is evaluating three different expansion plans: Minor, moderate or major. They can, of course, also do nothing. Long term profitability depends on future demand growth for the chemical compound. The following payoff table gives the present worth of future profitability (in $1,000) estimated by Unidyde management. Please make the optimal decision based on each of the following criteria. SHOW WORK.
Expansion Plan Demand Growth
High Medium Low
None 0 0 0
Minor 135 130 110
Moderate 150 250 -300
Major 210 120 -500
Maximax
Expansion
(Payoff) Demand Growth Decision Criterion
High Medium Low
None 0 0 0
Minor 135 130 110
Moderate 150 250 -300
Major 210 120 -500
Decision:
The Principle of Insufficient Reason
Expansion
(Payoff) Demand Growth Decision Criterion
High Medium Low
None 0 0 0
Minor 135 130 110
Moderate 150 250 -300
Major 210 120 -500
Decision:
(5 Points) Minimax Regret (First develop the regret table)
Expansion
(Regret) Demand Growth Decision Criterion
High Medium Low
None
Minor
Moderate
Major
Decision:
Expected Monetary Value
Expansion
(Payoff) Demand Growth Decision Criterion
High Medium Low
None 0 0 0
Minor 135 130 110
Moderate 150 250 -300
Major 210 120 -500
Probability 0.3 0.4 0.3
Decision:
Section IV: Linear Programming (20 Points)
Awesome Screen Inc. manufactures computer monitors in both 21" and 27" models. Each 21" model makes a profit of $120, and each 27" model makes a profit of $150. Both models utilize the same resources: labor and ray-guns. Each 21" model requires 4 labor hours and 1 ray-gun. And each 27" model requires 6 labor hours and 1 ray-gun. There are a total of 5,600 labor hours and a total of 1,200 ray-guns available each month. Awesome Screen Inc. has already promised to deliver 200 units of 21" model. How should Awesome Screen Inc. make its production decisions in order to maximize its total profit?
Please formulate the linear programming model and solve this problem with graphical methods.
Define the two variables
Write the objective function
Write ALL the constraints
Use graphical methods to SOLVE the problem. Specifically, shade the feasible region, mark and find the corner points of the feasible region, and find the optimal solution.
Section V: Differential Calculus
For a certain production facility, the cost function is C(x)=3x+5, and the revenue function is R(x)=20x-?2x?^2-3, where x is the number of units (in thousands) produced. C(x) and R(x) are measured in millions of dollars. Please answer the following questions.
Find the profit function P(x).
Find the break-even point(s) in terms of quantity x.
Find the marginal profit P'(x).
Find the quantity x that maximizes the profit.
Section VI: Forecasting
Consider the following time series representing quarterly sales of dishwashers at Big Boys Appliances over the past two years:
Time Sales Time Sales
2010 Q 1 25 2011 Q 1 76
2010 Q 2 86 2011 Q 2 125
2010 Q 3 64 2011 Q 3 105
2010 Q 4 30 2011 Q 4 90
Answer the following questions. Show ALL calculations.
Forecast the demand for dishwashers using a three-period weighted moving average with weights 4 assigned to the most recent period, and 2 and 1 assigned to two periods ago and three periods ago, respectively.
Time Sales Forecast Absolute Deviation
2010 Q1 25
2010 Q2 86
2010 Q3 64
2010 Q4 30
2011 Q1 76
2011 Q2 125
2011 Q3 105
2011 Q4 90
Forecast the demand for dishwashers using exponential smoothing with α=0.4. Use 2010 Q1 Sales as the forecast for 2010 Q2.
Time Sales Forecast Absolute Deviation
2010 Q1 25
2010 Q2 86
2010 Q3 64
2010 Q4 30
2011 Q1 76
2011 Q2 125
2011 Q3 105
2011 Q4 90
Based on the forecast errors from the 4th Quarter in 2010, which forecasting method is better? And why?