3 Questions_REDO***Quantitative Methods**Advanced Statistics

#4

#4 Midwestern Hardware must decide how many snow shovels to order for the coming snow season. Each shovel costs $14.00 and is sold for $29.95. No inventory is carried from one snow season to the next. Shovels unsold after February are sold at a discount price of $9.00. Past data indicate that sales are highly dependent on the severity of the winter season. Past seasons have been classified as mild or harsh, and the following distribution of regular price demand has been tabulated: Shovels must be ordered from the manufacturer in lots of 250. Construct a decision tree to illustrate the components of the decision model, and find the optimal quantity for Midwestern to order if the forecast calls for a 72% chance of a harsh winter. [Hint: Develop an Order-Demand matrix showing the profit on each order-demand combination. Because Decision Tree is limited to 5 initial branches, use order sizes of 500, 1500, 2500, 2750, and 3000.]

In this case during a Harsh winter it is best to buy 3100 shovels to yield maximum profit and in the case of a Mild winter there is no other alternate option but to buy 400 shovels.

#6

#6 A department store chain is planning to open a new store. It needs to decide how to allocate the 125,000 square feet if available floor space among seven departments. Data on expected performance of each department per month, in terms if square feet (sf), are shown in the table. The company has gathered $25 million to invest in floor stock. The risk column is a measure of risk associated with investment in floor stock based on past data from other stores and accounts for outdated inventory, pilferage, breakage, etc. For instance, electronics loses 24% of its total investment; furniture loses 12% of its total investment, etc. The maximum total risk can be no greated than 12% of the actual investment. a. Develop a linear optimization model to maximize profit. b. If the chain obtains another $2.5 million of investment capital for stock, what would the new solution be?

#7

#7 Sue Strand manages a professional theater group in a major city. Her marketing plan is focused on generating additional local demand for plays and increasing ticket revenue, and also gaining attention to the national level to build awareness of the theater group across the country. She has $35,000 to spend on media advertising. The goal of the advertisement campaign is to generate as much local recognition as possible while reaching at least 4,500 units national exposure. She has set a limit of 125 total ads. Additional information shown in the table to the right. The last column sets limits on the number if ads to ensure that the advertising markets do not become saturated. a. Find the optimal number of ads of each type to run to meet the choir’s goals by developing and solving an integer optimization model. b. What if she decides to use no more than six different types of ads? Modify the model in part (a) to answer this question.