To protect soil from erosion, some farmers plant winter cover crops such as winter wheat and rye. In addition to conserving soil, cover crops often increase crop yields in the row crops that follow in spring and summer. Suppose that a farmer has 800 acres of land and plans to plant winter wheat and rye. The input cost for I acre for each crop is given in the table along with the cost for machinery and labor. The profit for 1 acre of each crop is given in the last column.
Input Cost per Acre | Labor/Machinery Cost per Acre | Profit per Acre | |
---|---|---|---|
Wheat | $90 | $50 | $42 |
Rye | $120 | $40 | $35 |
Suppose the farmer has budgeted a maximum of $90,000 for input costs and a maximum of $36,000 for labor and machinery.
a. Determine the number of acres of each crop that the farmer should plant to maximize profit. (Assume that all crops will be sold.)
b. What is the maximum profit?
c. If the profit per acre for wheat were $40 and the profit per acre for rye were $45, how many acres of each crop should be planted to maximize profit?
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
College Algebra (Collegiate Math)
- If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.arrow_forwardRedo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage