Algebraic formulation of the linear programming model

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Reference no: EM13105868

GoodBuy Inc. is a small electronics company that manufactures cell phones and digital recorders. The per-unit labor costs, raw material costs, and selling price of each product are given below. On December 1, 2008, GoodBuy has available raw material that is sufficient to manufacture 100 cell phones and 100 recorders. On the same date, the company's balance sheet is as shown in the table below. GoodBuy's asset/liability ratio (called the current ratio) is 20,000/10,000 = 2.

GoodBuy must determine how many cell phones and recorders should be produced during December. Demand is large enough to ensure that all goods produced will be sold. All sales are on credit, however, and payment for goods produced in December will not be received until February 1, 2009. During December, GoodBuy will collect $2000 in accounts receivable, and GoodBuy must pay off $1000 of the outstanding loan and a monthly rent of $1000. On January 1, 2009, GoodBuy will receive a shipment of raw material worth $2000, which will be paid for on February 1, 2009.

GoodBuy's management has decided that the cash balance on January 1, 2009 must be at least $4000. To maintain its current favorable credit status, GoodBuy's bank requires that the current ratio at the beginning of January be at least 2. To maximize the contribution to profit from December production, (revenues to be received - variable production costs), what should GoodBuy produce during December?

Cost Information for GoodBuy

	Cell Phones	Recorders
Selling Price	$100	$90
Labor Cost	$50	$35
Raw Material Cost	$30	$40

Balance Sheet for GoodBuy

	Assets	Liabilities
Cash	$10,000
Accounts Receivable¹	$3,000
Inventory Outstanding²	$7,000
Bank Loan		$10,000

1 - Accounts receivable is money owed to GoodBuy by customers who have previously purchased GoodBuy products.

2 - Value of December 1, 2008 inventory = 30(100) + 40(100) = $7000.

Hints and Suggestions

You must determine how many cell phones and digital recorders to produce during December. Thus, you should define:

X₁ = number of cell phones produced during December

X₂ = number of digital recorders produced during December

There are two constraints based on the availability of raw materials. In addition, GoodBuy faces the following two constraints:
- Cash on hand on January 1, 2009 must be at least $4000.

January 1 cash on hand = December 1 cash on hand

+ accounts receivable collected during December

portion of loan repaid during December - December rent

- December labor costs.

(January 1 assets)/(January 1 liabilities) ? 2 must hold.

Important Relationships

January 1 asset position = January cash position

+ January 1 accounts receivable + January 1 inventory position.

January 1 cash position = 10,000 - 50x₁ - 35x₂

January 1 accounts receivable = December 1 accounts receivable

+ accounts receivable from December sales

- accounts receivable collected during December.

Value of January 1 inventory = value of December 1 inventory

- value of inventory used in December

+ value of inventory received on January 1.

January 1 liabilities = December 1 liabilities - December loan payment

+ amount due on January 1 inventory shipment.

Your mathematical result should be:

X₁ = 50 cell phones

X₂ = 100 digital recorders

Maximum profit = $2500.

I need the below answered. Maybe not the report, but just a small conclusion I can add to.

Deliverables:

A complete algebraic formulation of the linear programming model. This should include a description of the decision variables and an explanation of the objective function and constraints.
Computer output of your solution and ranging from POM-QM. This must be printed from POM-QM.
A report (MS-Word document) to management describing your objective and production plan. The report should be written clearly, concisely, and accurately. It should fit on a single page. Many young professionals believe that they will be evaluated entirely on whether the numbers are right and this is simply not true. Managers are busy people who have little time or patience to wade through poorly written reports. You will be graded on both grammatical and technical accuracy.

Reference no: EM13105868

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