The following table is the result of one or more iterations.

Complete the next iteration using the stepping-stone method.

Consider the transportation table below. The solution displayed was obtained by performing some iterations of the transportation method on this problem. What is the total cost of the shipping plan that would be obtained by performing one more iteration of the stepping-stone method on this problem?

Refer to the table that follows.

Use the intuitive lowest-cost approach to find an initial feasible solution. Is this approach better than the northwest-corner method?

The following time series shows the sales of a particular product over the past 12 months.

$$\begin{matrix} \text{Month} & \text{Sales} & \text{Month} & \text{Sales}\\ \hline \text{1} & \text{105} & \text{7} & \text{145}\\ \text{2} & \text{135} & \text{8} & \text{140}\\ \text{3} & \text{120} & \text{9} & \text{100}\\ \text{4} & \text{105} & \text{10} & \text{80}\\ \text{5} & \text{90} & \text{11} & \text{100}\\ \text{6} & \text{120} & \text{12} & \text{110}\\ \end{matrix}$$

a. Construct a time series plot. What type of pattern exists in the data? b. Use $\alpha =$ .3 to compute the exponential smoothing forecasts for the time series. c. Use a smoothing constant of $\alpha =$ .5 to compute the exponential smoothing forecasts. Does a smoothing constant of .3 or .5 appear to provide more accurate forecasts based on MSE?

Consider the following network representation of a transportation problem:

The supplies, demands, and transportation costs per unit are shown on the network. What is the optimal (cost minimizing) distribution plan?

Find an initial solution to the following transportation problem.

Using the stepping-stone method, find the optimal solution. Compute the total cost.

Allen Air Conditioning manufactures room air conditioners at plants in Houston, Phoenix, and Memphis. These are sent to regional distributors in Dallas, Atlanta, and Denver. The shipping costs vary, and the company would like to find the least-cost way to meet the demands at each of the distribution centers. Dallas needs to receive 800 air conditioners per month, Atlanta needs 600 , and Denver needs 200 . Houston has 850 air conditioners available each month. Phoenix has 650 , and Memphis has 300 . The shipping cost per unit from Houston to Dallas is $\$ 8$, to Atlanta $\$ 12$, and to Denver S10. The cost per unit from Phoenix to Dallas is $\$ 10$, to Atlanta $\$ 14$, and to Denver $\$ 9$. The cost per unit from Memphis to Dallas is $\$ 11$, to Atlanta S8, and to Denver S12. How many units should owner Stephen Allen ship from each plant to each regional distribution center? What is the total transportation cost? (Note that a "dummy" destination is needed to balance the problem.)

Corporate triple-A bond interest rates for 12 consecutive months follow.

$$\begin{matrix} \text{9.5} & \text{9.3} & \text{9.4} & \text{9.6} & \text{9.8} & \text{9.7} & \text{9.8} & \text{10.5} & \text{9.9} & \text{9.7} & \text{9.6} & \text{9.6}\\ \end{matrix}$$

a. Construct a time series plot. What type of pattern exists in the data? b. Develop three-month and four-month moving averages for this time series. Does the three-month or four-month moving average provide more accurate forecasts based on MSE? Explain. c. What is the moving average forecast for the next month?

Refer to the table that follows.

Find the optimal solution using the stepping-stone method.

Suppose a linear programming (maximation) problem has been solved and that the optimal value of the objective function is $\$ 300$. Suppose an additional constraint is added to this problem. Explain how this might affect each of the following:

The feasible region.

Refer to the table that follows.

Use the northwest-corner method to find an initial feasible solution. What must you do before beginning the solution steps?

Consider the transportation table at right. Unit costs for each shipping route are in dollars. What is the total cost of the basic feasible solution that the intuitive lowest-cost method would find for this problem? $\hspace{4cm}$Destination

For the following Gregory Bier Corp. data, find the starting solution and initial cost using the northwest-corner method. What must you do to balance this problem?

What are the steps in the intuitive lowest-cost method?