MY-ASSIGNMENTEXPERT™可以为您提供 gallaudet.edu MTH360 Operations research运筹学的代写代考和辅导服务！
Math113课程简介
Operations research (British English: operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-makingMathematical modeling under conditions of certainty and uncertainty. Linear programming, duality, and sensitivity analysis. Markov chains and other stochastic processes. Applications to problems in transportation, scheduling, and resource allocation. Offered every year. Prerequisites: MTH 204 or MTH 302.
Prerequisites
Operational research (OR) encompasses the development and the use of a wide range of problem-solving techniques and methods applied in the pursuit of improved decision-making and efficiency, such as simulation, mathematical optimization, queueing theory and other stochastic-process models, Markov decision processes, econometric methods, data envelopment analysis, ordinal priority approach, neural networks, expert systems, decision analysis, and the analytic hierarchy process
This course covers linear programming, the simplex algorithm, duality theory and sensitive analysis, network analysis, transportation, assignment, game theory, inventory theory, and queuing theory.
Prerequisites: MAT 140, or MAT 150; or permission of the instructor
Program: Mathematics
Credit: 3
MTH360 Operations research HELP（EXAM HELP， ONLINE TUTOR）
Linear Programming Model Formulation: Formulate a Linear Programming model for each problem below, and solve it using LINDO (available on the HP-UX workstations, or you may use the software packaged with the textbook.) Be sure to state precisely the definitions of your decision variables, and explain in a few words the purpose of each type of constraint. Write a few words to state what the optimal solution is (i.e., without making use of variable names). (For instructions on LINDO, see $\$ 4.7$ and the appendix of chapter 4 of the text.)
Exercise #4, page 113 (Walnut Orchard Farms)
“Walnut Orchard has two farms that grow wheat and corn. Because of differing soil conditions, there are differences in the yields and costs of growing crops on the two farms. The yields and costs are
Farm 1
Farm 2
$\begin{array}{lcc}\text { Corn yield/acre } & 500 \text { bushels } & 650 \text { bushels } \ \text { Cost/acre of corn } & \$ 100 & \$ 120 \ \text { Wheat yield/acre } & 400 \text { bushels } & 350 \text { bushels } \ \text { Cost/acre of wheat } & \$ 90 & \$ 80\end{array}$
Each farm has 100 acres available for cultivation; 11,000 bushels of wheat and 7000 bushels of corn must be grown. Determine a planting plan that will minimize the cost of meeting these demands.
To minimize the cost of meeting the demand, we need to find out how many acres of each crop should be planted on each farm to produce the required yield of wheat and corn at minimum cost.
Let x be the number of acres of corn to be planted on Farm 1, y be the number of acres of corn to be planted on Farm 2, z be the number of acres of wheat to be planted on Farm 1, and w be the number of acres of wheat to be planted on Farm 2.
The objective is to minimize the total cost C: \begin{align*} C &= 100x + 120y + 90z + 80w \ &= 100(x+z) + 120(y+w) \ \end{align*}
Subject to the following constraints:
- The total yield of corn: \begin{align*} 500x + 650y &= 7000 \ x + y &= \frac{7000}{500} + \frac{7000}{650} \approx 25.54 \end{align*}
- The total yield of wheat: \begin{align*} 400z + 350w &= 11000 \ z + w &= \frac{11000}{400} + \frac{11000}{350} \approx 44.29 \end{align*}
- The non-negativity constraints: \begin{align*} x, y, z, w &\geq 0 \ \end{align*}
Since x, y, z, and w must be non-negative, we can assume that the decimal parts of x+y and z+w represent the proportions of the crops planted on each farm. Thus, we can assign x+y = 26 (rounded up from 25.54) and z+w = 45 (rounded up from 44.29) to simplify the problem.
Then, we can rewrite the constraints as: \begin{align*} 500x + 650y &= 7000 \ 400z + 350w &= 11000 \ x + z &= 13 \ y + w &= 32 \ \end{align*}
Investment planning
I now have $\$ 100$. The following investments are available at the beginning of each of the next five years:
Investment A: Every dollar invested yields $\$ 0.10$ a year from now and $\$ 1.30$ three years after the original investment, a total of $\$ 1.40$.
To make an investment plan, we need to determine the optimal amount to invest in Investment A each year for the next five years to maximize the total return. Let $x_i$ be the amount invested in year $i$, where $i = 1,2,3,4,5$.
We can set up the objective function to maximize the total return as follows:
\begin{align*} \max \quad & 0.10x_1 + 0.10x_2 + 0.10x_3 + 0.10x_4 + 0.10x_5 + 1.30x_4 + 1.30x_5 + 100 \ \end{align*}
The first five terms represent the returns one year after each investment, and the last two terms represent the returns three years after investments made in years 4 and 5. The constant term of 100 represents the initial investment.
We also need to add constraints to ensure that we do not invest more than we have and that we invest the entire amount available each year:
\begin{align*} \sum_{i=1}^5 x_i &\leq 100 \ x_i &\geq 0, \quad i = 1,2,3,4,5 \ \end{align*}
Note that we do not need to include a constraint for year 4 or 5 to account for the three-year return, as those terms are already included in the objective function.
MY-ASSIGNMENTEXPERT™可以为您提供UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN MATH2940 linear algebra线性代数课程的代写代考和辅导服务！ 请认准MY-ASSIGNMENTEXPERT™. MY-ASSIGNMENTEXPERT™为您的留学生涯保驾护航。
