Howie’s Carpet World has just received an order for carpets for a new office building. The order is for 4,000 yards of carpet 4-feet wide, 20,000 yards of carpet 9-feet wide, and 9,000 yards of carpet 12-feet wide. Howie can buy 2 kinds of carpet rolls from his supplier, namely 14 feet wide carpet and 18 feet wide; and Howie will cut the carpet for the new office building order from whatever carpet he buys from his supplier. The 14 feet wide carpeting comes in rolls of 100-yards long and costs $1,000 per roll; the 18 feet wide carpeting also comes in rolls of 100-yards long, but it costs $1,400 per roll. Howie needs to determine how many of the two types of carpet rolls to buy from his supplier and how they should be cut in order to minimize his cost of filling the order. Howie will throw away any of the carpet not used after cutting. Refer to Unit 5 Slide 9 for consideration of cutting patterns.

2) in order to obtain the 20,000 yards of 9 ft wide carpet, the company must purchase 10,000 yards of 18 ft wide carpet = (10,000 / 100) x $1,400 = $140,000

1) if you buy 1,000 more yards of 18 ft wide carpet, you will be able to get the 4,000 yards of 4 ft wide = (1,000 / 100) x $1,400 = $14,000.

You could also purchase 1,400 yards of the 12 ft wide carpet (you will also get the 4,000 yards that you need) at the same cost = (1,400 / 100) x $1,000 = $14,000

3) finally you must purchase 9,000 yards of 14 ft wide carpet to get the remaining 9,000 yards of 12 ft wide carpet = (9,000 / 100) x $1,000 = $90,000

total cost = $140,000 + $14,000 + $90,000 = $244,000