• ErgoPillow is an online shop selling two different models of ergonomic pillow which helps to relieve sore necks. It sells the deluxe and premium versions for $50 and $80 each. The deluxe pillow is imported from a supplier in India while the premium pillow is imported from a supplier in Thailand. The finance team has informed us that both pillow models give the same profit of $10 per pillow.

The pillows are sent via ocean freight in containers and each container can carry up to 1,000 pillows. The sales team has forecasted that the aggregated sales is 50 containers of pillows in a year and must make advance arrangements to order from the suppliers and book the shipment due to two considerations: long shipment time and potential loss due to piracy. Order is by container units and orders can be placed throughout the year.

The shipment time is 16 days and 7 days from India and Thailand, respectively. ErgoPillow has requested for the average shipping time for its orders to be capped at 10 days maximum. The shipping cost per pillow from India and Thailand is 20% and 10% of the pillow selling price, respectively. Also, 8% of orders from Thailand are lost due to piracy while India suffers a loss of 4% of its orders annually. The management is willing to accept nothing more than 8 orders gone missing due to piracy. To ensure stable supply, at least 30% of its orders must be placed with each supplier.

ErgoPillow management is very particular about the shipping cost and would like you to recommend how the orders should be placed between the two suppliers. State qualitatively the objective, decision variables, and constraints. Then formulate the problem as an LP model. After that, solve it using the graphical solution procedure. Please limit the answer to two pages.

• The supplier in India would like to boost their sales with ErgoPillow and they proposed to reduce their shipment time with no additional cost. Apply the appropriate LP concept and show whether this proposal might work or not.
• Your company is a business consulting company that advises companies on optimizing their operations using LP. You are invited to your child’s primary school class where parents are invited to share about what they do for a living.