Explanation of Solution
Given data:
The farmer Jane owns 45 acres of land and planning to plant with wheat or corn.
On planting wheat she yields $200 profit and corn yields $300 profit.
Given table:
Wheat | Corn | |
Labor | 3 workers | 2 workers |
Fertilizer | 2 tons | 4 tons |
Consider
Objective function:
Considering the constraints,
Constraint 1: Total acres of land used
Constraint 2: Maximum number of workers to be used is 100
Constraint 3: Maximum tons of fertilizers are 120 tons.
Expressing the constraint 1 in terms of
Expressing the constraint 2 in terms of
Expressing the constraint 3 in terms of
Therefore, the mathematical model of given LP is,
Subject to the constraints,
Converting the inequality constraint without adding any variable:
The coordinate points for the constraint
If
If
The coordinate points for the constraint
If
If
The coordinate points for the constraint
If
If
Therefore, the coordinate point for the constraint
Graph:
From the above graph, it is known that the vertices of the feasible region lies in the points
Calculating the value of the objective function to find the end points:
Therefore, the value of
Substituting the value of
Trending nowThis is a popular solution!
Chapter 3 Solutions
Operations Research : Applications and Algorithms
- A person is cutting a long board of wood into different length of pieces . Each cutting has fixed width 2 cm lengths. Given that each cutting with different length has a different price, Now, we are required to help this person to find the optimal cuts in order to increase his income. Consider following example showing different cut’s lengths and their equivalent prices. Input: board length = 4 Length [ ] = [1, 2, 3, 4, 5, 6, 7, 8] Price [ ] = [2, 6, 8, 10, 14, 17, 19, 20] Output: Best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12 [Explanation: the possible cuts and profit of each is as follows: As noted the best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12arrow_forwardAt the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit.arrow_forwardAt the beginning of month 1, Finco has $400 in cash. At the beginning of months 1, 2, 3, and 4, Finco receives certain revenues, after which it pays bills (see Table 2 below). Any money left over may be invested for one month at the interest rate of 0.1% per month; for two months at 0.5% per month; for three months at 1% per month; or for four months at 2% per month. Use linear programming to determine an investment strategy that maximizes cash on hand at the beginning of month 5. Formulate an LP to maximize Finco’s profit. Table 2 Month Revenues ($) Bills ($) 1 400 600 2 800 500 3 300 500 4 300 250arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole