The queen city nursery manufactures bags of potting soil from compost and topsoil. each cubic foot of compost costs 12 cents (enter as .12) and contains 4 pounds of sand, 3 pounds of clay, and 5 pounds of humus. each cubic foot of topsoil costs 20 cents (enter as .20) and contains 3 pounds of sand, 6 pounds of clay, and 12 pounds of humus. each bag of potting soil must contain at least 12 pounds of sand, at least 12 pounds of clay, and at least 10 pounds of humus. formulate the problem as a linear program and find the best combination of compost and topsoil that meets the stated conditions at the lowest cost per bag.