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 () Volume (cubic meters) 0.000768 Product One vacuum-packed candle (contains 24 tea candles) Standard pillow (50x90cm) 6.99 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.

Explanation / Answer

c)

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

The constraints are of capacity of the 45' high cube container ( weight and volume)

Mathematical representation is as below

0.96x1+ 1.23x2 <=25,600 and it is the weight capacity constraint of the container

0.000768x1 + 0.026x2 <= 86 and it is the volume capacity constraint of the container

d)

Yes there are sign constraint as well as below because the number of pillows or vacuum packed candle shipped cannot be negative, so the mathematical representation is as below

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

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