Problem Consider the following information about two of IKEA\'s products: candle

Question

Problem Consider the following information about two of IKEA's products: candles and pillows. Weight (kilograms) 0.96 Unit Price (S) Volume (cubic meters) 0.000768 Product 6.99 One vacuum-packed candle (contains 24 tea candles) Standard pillow (50x90cm) 1.23 0.026 19.99 Suppose IKEA uses standard 45' high cube containers in shipping. Vendor loads all goods to the container to be shipped to IKEA's facilities. A 45' high cube has limited weight and volume capacity: it can carry up to 25,600 kilograms in weight and accommodates up to 86 cubic meters in volume. You are asked to determine the optimal mix of products that should be loaded to each container so that IKEA maximizes the value of goods loaded (i.e. total revenue) without exceeding the weight or volume limit of a container. Formulate and solve a linear programming model to determine IKEA's optimal product mix a) What are the decision variables? Explain them in English and provide the mathematical notation. How many decision variables do you have? b) What is the objective function? Provide the verbal description and the mathematical representation.

Explanation / Answer

a)

The decision variable would be

1: How many Vacuum packed candle to be shipped and

2: How many standard pillow to be shipped

Mathematical notation of abouve decision variable are let

x1 is the number of Vacuum packed candle to be shipped and x2 is the number standard pillow to be shipped

So there are 2 decision variables

b)

Objective is Maximize the revenue of goods shipped under the constraints of capacity of the container ( weight and volue)

Mathematical representation is as below

Max : 6.99x1 + 19.99x2

Subject to

0.96x1+ 1.23x2 <=25,600 ( weight capacity constraint)

0.000768x1 + 0.026x2 <= 86 ( volume capacity constraint)

x1, x2 >=0 ( Numbers shipped cannot be negative)

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