A farmer has 1200 acres of land and plans 10 plant corn and soybeans. The input cost (cost of seed, fertilizer, herbicide, and insecticide) for 1 acre or each crop is given in the table along with the cost of 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 | |
---|---|---|---|
Corn | $180 | $80 | $120 |
Soybeans | $120 | $100 | $1000 |
Suppose the farmer has budgeted a maximum of $198,000 for input costs and a maximum of $110,000 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 were reversed between the two crops (that is, $100 per acre for corn and $120 per acre for soybeans), 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-ACCESS
- The variable cost of manufacturing a product is OMR 35 per unit. The fixed cost is OMR 2800. The capacity of the firm is 100 units. The selling price of the product is 120 per unit. What is the total profit if the firm sells 100 units? O a. RO 5700 O b. RO 12000 RO 6300 O d. RO 3500 Activate Windows Go to Settings to activate Windoarrow_forwardA picture frame costs $2 per square unit present on the outside of the picture frame (the shaded region). If a picture frame has dimensions as shown below, what will be the total cost of this picture frame? 12 20 14 O $368 O $415 O $418 $212arrow_forwardAn anticlot drug can be made for $13 per unit. The total cost to produce 100 units is $1,750. What are the fixed costs? 450 1200 1300 O 550 O 1750arrow_forward
- A product costing $350, less 30%, 20%, and 10%, sells to allow for overhead expenses of 30% of the selling price and profit of 20% of the selling price. During a sale, the product is marked down by 40%. What is the sale price?arrow_forwardSolve. 3 5 8 4.arrow_forwardIn case of LSD, each row and each column should be a complet Column. Block. Row. Designarrow_forward
- Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch. A 3-column table with 5 rows. Column 1 is labeled Friend with entries 1, 2, 3, 4, 5. Column 2 is labeled Model A with entries 150, 143, 108, 145, 128. Column 3 is labeled Model B with entries 228, 123, 212, 137, 174. The mean of the differences is 40 inches, and the standard deviation of the differences is 53.57 inches. The conditions for inference are met. A 90% confidence interval for the mean difference (B – A) in flight distance is –11.08 inches to 91.08 inches. What is the correct interpretation of this interval? The…arrow_forwardThe fixed costs incurred by a small genetics research lab are $200,000 per year. Variable costs are 60% of the annual revenue. If annual revenue is $300,000, determine the annual profit (loss).arrow_forwardThe Conference Company supplies tables for conferences. Each table is a rectangle. Each table can seat one person at its short edge and two people at its long edge. The diagrams below show how these tables can be arranged for different numbers of people. No one sits inside the arrangements. Size 1 Size 2 Size 3 4 tables 6 tables 12 people 16 people 1. How many tables are in a Size 3 arrangement? tables 2. How many tables are in a Size 7 arrangement? tables 3. Write down a rule or formula for working out how many tables there are when you know the size number.arrow_forward
- The expenses and income of an individual are given in table form to the right. Find the net monthly cash flow (it may be negative or positive). Assume that amounts shown for salaries and wages are after taxes and that 1 month= 4 weeks. Income Part-time job: $1400/month Student loans: $6600/year Scholarship: $5500/year The net monthly cash flow is $ (Round to the nearest dollar as needed.) Expenses Rent: $550/month Groceries: $40/week Tuition and fees: $7500/year Health insurance: $40/month Entertainment: $300/month Phone: $70/month CINCIarrow_forwardTask 2arrow_forwardCaseDesigncompany assembles cabinets and drawers. They earn a profit of 1400 pesos ineach cabinet and 850 pesos in each drawer. There were 200 hours available timefor assembling. Each cabinet requires 2hrs to be assembled and 3hoursassembling time for each drawer. Cabinet can be painted in 2hrs while drawercan be painted in 1hr. There were 100 hours available.Questions:1. How many units of cabinet and drawerthey should assemble to maximize the profit provided that they must assembledboth?2. How much is the maximum profit?arrow_forward
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL