A gardener has 1,000 square yards of land available to devote to cash crops. Profits expected by crop are: $20 per square yards for lima beans, $10 per 10 square yards for spinach, and $15 per 10 square yards for zucchini.
The gardener has $200 available for investment. Total preparation cost for 10 square yards are $4 for lima beans, $2 for spinach, and $1 for zucchini. The gardener has 200 hours available for gardening. Each 10 square yards requires 2 hours for lima beans, 1 hour for spinach, and 3 hours for zucchini.
a. Formulate a linear programming model to determine the optima areas in square yards for each of the three crops.
b. Solve three iterations of the simplex method for this model.