Washington State Math Council

You have just bought a home in the country which has 10 acres of farm land. (1 acre = 43,560 sq. ft.) You want to plant vegetables on your farm, so you drive to the Farmville Feed Store to buy seed. On the wall at the feed store is this list of vegetables, the weight of each sack of seed, and how much area a sack covers.

 VEGETABLE EACH SACK WEIGHS EACH SACK COVERS Corn 100 pounds 10,000 sq. ft. Soybeans 100 pounds 85,000 sq. ft. Squash 50 pounds 32,500 sq. ft. Green beans 75 pounds 22,500 sq. ft. Peas 75 pounds 13,100 sq. ft.

You can only buy whole sacks of seeds. You are a very thrifty farmer and don't want to waste seed! You drove to Farmville in a pickup truck which can carry 1000 pounds. Farmville is a long way from your farm, so you want to take all your seed back in only 1 trip. So, the total weight of all your seed must not exceed 1000 pounds.

Your job is to plan your farm. Decide what vegetables you want to plant and how many sacks of seed you need of each vegetable so that you plant as much of your 10 acres as you can and have as little seed as possible left over. It must all fit in a 1000 pound pick-up truck. You don't have to plant every vegetable. The best solution fills 10 acres with no seed left over and weighs 1000 pounds or less.