Need help with my Mathematics question – I’m studying for my class.

Minimum of five pages including a cover page with all necessary info. Clearly identify the Case Problem # and titles. Include a reference page. The main body should clearly address all questions asked in the managerial report of the two case problems. This essay should reflect scholarly writing and current APA standards and must include citations to support the ideas.

Final Project Part A, select one of the cases from the list below

Ch. 4 Linear Programming Applications in Marketing, Finance, and Operations Management: Case#1

Case Problem 1

Planning an Advertising Campaign

The Flamingo Grill is an upscale restaurant located in St. Petersburg, Florida. To help plan an advertising campaign for the coming season, Flamingo’s management team hired the advertising firm of Haskell & Johnson (HJ). The management team requested HJ’s recommendation concerning how the advertising budget should be distributed across television, radio, and online advertisements. The budget has been set at $279,000.

In a meeting with Flamingo’s management team, HJ consultants provided the following information about the industry exposure effectiveness rating per ad, their estimate of the number of potential new customers reached per ad, and the cost for each ad:

Advertising Media | Exposure Rating per Ad | New Customers per Ad | Cost per Ad

Television | 90 | 4,000 | $10,000

Radio | 25 | 2,000 | $ 3,000

Online | 10 | 1,000 | $ 1,000

The exposure rating is viewed as a measure of the value of the ad to both existing customers and potential new customers. It is a function of such things as image, message recall, visual and audio appeal, and so on. As expected, the more expensive television advertisement has the highest exposure effectiveness rating along with the greatest potential for reaching new customers.

At this point, the HJ consultants pointed out that the data concerning exposure and reach were only applicable to the first few ads in each medium. For television, HJ stated that the exposure rating of 90 and the 4000 new customers reached per ad were reliable for the first 10 television ads. After 10 ads, the benefit is expected to decline. For planning purposes, HJ recommended reducing the exposure rating to 55 and the estimate of the potential new customers reached to 1500 for any television ads beyond 10. For radio ads, the preceding data are reliable up to a maximum of 15 ads. Beyond 15 ads, the exposure rating declines to 20 and the number of new customers reached declines to 1200 per ad. Similarly, for online ads, the preceding data are reliable up to a maximum of 20; the exposure rating declines to 5 and the potential number of new customers reached declines to 800 for additional ads.

Flamingo’s management team accepted maximizing the total exposure rating, across all media, as the objective of the advertising campaign. Because of management’s concern with attracting new customers, management stated that the advertising campaign must reach at least 100,000 new customers. To balance the advertising campaign and make use of all advertising media, Flamingo’s management team also adopted the following guidelines:

Use at least twice as many radio advertisements as television advertisements.

Use no more than 20 television advertisements.

The television budget should be at least $140,000.

The radio advertising budget is restricted to a maximum of $99,000.

The online budget is to be at least $30,000.

HJ agreed to work with these guidelines and provide a recommendation as to how the $279,000 advertising budget should be allocated among television, radio, and online advertising.

Managerial Report

Develop a model that can be used to determine the advertising budget allocation for the Flamingo Grill. Include a discussion of the following in your report:

A schedule showing the recommended number of television, radio, and online advertisements and the budget allocation for each medium. Show the total exposure and indicate the total number of potential new customers reached.

How would the total exposure change if an additional $10,000 were added to the advertising budget?

A discussion of the ranges for the objective function coefficients. What do the ranges indicate about how sensitive the recommended solution is to HJ’s exposure rating coefficients?

After reviewing HJ’s recommendation, the Flamingo’s management team asked how the recommendation would change if the objective of the advertising campaign was to maximize the number of potential new customers reached. Develop the media schedule under this objective.

Compare the recommendations from parts 1 and 4. What is your recommendation for the Flamingo Grill’s advertising campaign?

Final Project Part B, select one of the cases from the list below

Ch.10 Inventory Models: Case#1

Case Problem 1

Wagner Fabricating Company

Managers at Wagner Fabricating Company are reviewing the economic feasibility of manufacturing a part that the company currently purchases from a supplier. Forecasted annual demand for the part is 3200 units. Wagner operates 250 days per year.

Wagner’s financial analysts established a cost of capital of 14% for the use of funds for investments within the company. In addition, over the past year $600,000 was the average investment in the company’s inventory. Accounting information shows that a total of $24,000 was spent on taxes and insurance related to the company’s inventory. In addition, an estimated $9000 was lost due to inventory shrinkage, which included damaged goods as well as pilferage. A remaining $15,000 was spent on warehouse overhead, including utility expenses for heating and lighting.

An analysis of the purchasing operation shows that approximately two hours are required to process and coordinate an order for the part regardless of the quantity ordered. Purchasing salaries average $28 per hour, including employee benefits. In addition, a detailed analysis of 125 orders showed that $2375 was spent on telephone, paper, and postage directly related to the ordering process.

A one-week lead time is required to obtain the part from the supplier. An analysis of demand during the lead time shows it is approximately normally distributed with a mean of 64 units and a standard deviation of 10 units. Service-level guidelines indicate that one stock-out per year is acceptable.

Currently, the company has a contract to purchase the part from a supplier at a cost of $18 per unit. However, over the past few months, the company’s production capacity has been expanded. As a result, excess capacity is now available in certain production departments, and the company is considering the alternative of producing the parts itself.

Forecasted utilization of equipment shows that production capacity will be available for the part being considered. The production capacity is available at the rate of 1000 units per month, with up to five months of production time available. Management believes that with a two-week lead time, schedules can be arranged so that the part can be produced whenever needed. The demand during the two-week lead time is approximately normally distributed, with a mean of 128 units and a standard deviation of 20 units. Production costs are expected to be $17 per part.

A concern of management is that setup costs will be substantial. The total cost of labor and lost production time is estimated to be $50 per hour, and a full eight-hour shift will be needed to set up the equipment for producing the part.

Managerial Report

Develop a report for management of Wagner Fabricating that will address the question of whether the company should continue to purchase the part from the supplier or begin to produce the part itself. Include the following factors in your report:

An analysis of the holding costs, including the appropriate annual holding cost rate

An analysis of ordering costs, including the appropriate cost per order from the supplier

An analysis of setup costs for the production operation

A development of the inventory policy for the following two alternatives:

Ordering a fixed quantity Q from the supplier

Ordering a fixed quantity Q from in-plant production

Include the following in the policies of parts 4(a) and 4(b):

Optimal quantity Q*

Number of order or production runs per year

Cycle time

Reorder point

Amount of safety stock

Expected maximum inventory

Average inventory

Annual holding cost

Annual ordering cost

Annual cost of the units purchased or manufactured

Total annual cost of the purchase policy and the total annual cost of the production policy

Make a recommendation as to whether the company should purchase or manufacture the part. What savings are associated with your recommendation as compared with the other alternative?