Question

Write the detailed definition of a supply chain/logistics related maximization problem with 8 variables and 6 constraints. Each constraint should have at least 6 variables. Each constraint should have At least 5 variables will have a value greater than zero in the resulting solution. Variables may have decimal values. Type of equations is less than equal. Numbers and types of variables and constraints are important and strict. Model the problem and verify that is feasible, bounded and have at least 5 variables are nonzero.

74

likes
372 views

Answer to a math question Write the detailed definition of a supply chain/logistics related maximization problem with 8 variables and 6 constraints. Each constraint should have at least 6 variables. Each constraint should have At least 5 variables will have a value greater than zero in the resulting solution. Variables may have decimal values. Type of equations is less than equal. Numbers and types of variables and constraints are important and strict. Model the problem and verify that is feasible, bounded and have at least 5 variables are nonzero.

Expert avatar
Esmeralda
4.7
95 Answers
To model the supply chain/logistics maximization problem with 8 variables and 6 constraints, we can use the following steps:

Step 1: Define the Decision Variables:
Let us denote the decision variables as follows:
x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8

Step 2: Formulate the Objective Function:
The objective of the problem is to maximize a certain quantity. Let's assume the objective function is given by:
\text{Maximize } Z = c_1x_1 + c_2x_2 + c_3x_3 + c_4x_4 + c_5x_5 + c_6x_6 + c_7x_7 + c_8x_8
where c_1, c_2, c_3, c_4, c_5, c_6, c_7, c_8 are the coefficients associated with the decision variables.

Step 3: Specify the Constraints:
We need to define 6 constraints such that each constraint has at least 6 variables and at least 5 variables will have a value greater than zero in the resulting solution. Let's represent the constraints as follows:

Constraint 1: a_{11}x_1 + a_{12}x_2 + a_{13}x_3 + a_{14}x_4 + a_{15}x_5 + a_{16}x_6 + a_{17}x_7 + a_{18}x_8 \leq b_1
Constraint 2: a_{21}x_1 + a_{22}x_2 + a_{23}x_3 + a_{24}x_4 + a_{25}x_5 + a_{26}x_6 + a_{27}x_7 + a_{28}x_8 \leq b_2
Constraint 3: a_{31}x_1 + a_{32}x_2 + a_{33}x_3 + a_{34}x_4 + a_{35}x_5 + a_{36}x_6 + a_{37}x_7 + a_{38}x_8 \leq b_3
Constraint 4: a_{41}x_1 + a_{42}x_2 + a_{43}x_3 + a_{44}x_4 + a_{45}x_5 + a_{46}x_6 + a_{47}x_7 + a_{48}x_8 \leq b_4
Constraint 5: a_{51}x_1 + a_{52}x_2 + a_{53}x_3 + a_{54}x_4 + a_{55}x_5 + a_{56}x_6 + a_{57}x_7 + a_{58}x_8 \leq b_5
Constraint 6: a_{61}x_1 + a_{62}x_2 + a_{63}x_3 + a_{64}x_4 + a_{65}x_5 + a_{66}x_6 + a_{67}x_7 + a_{68}x_8 \leq b_6

where each coefficient a_{ij} and the right-hand side b_i are known values.

Step 4: Verify the Problem Properties:
To verify the problem properties, we need to check the feasibility, boundedness, and ensure that at least 5 variables are non-zero.

- Feasibility: The problem is feasible if there exists a solution that satisfies all constraints. This can be checked by solving the linear programming problem and confirming the existence of a feasible solution.

- Boundedness: The problem is bounded if the objective function has a maximum value. This can also be determined by solving the linear programming problem and observing whether the objective function is finite.

- Non-zero Variables: By solving the linear programming problem, we can determine the values of the decision variables. We need to ensure that at least 5 variables have non-zero values in the resulting solution.

Once the problem is modeled and solved, we can obtain the solution by finding the optimal values of the decision variables. The final solution can be represented as:

Answer: The optimal solution to the supply chain/logistics maximization problem is x_1 = a_1, x_2 = a_2, x_3 = a_3, x_4 = a_4, x_5 = a_5, x_6 = 0, x_7 = 0, x_8 = 0 with an objective function value of Z = \text{Optimal Value}.

Frequently asked questions (FAQs)
How many distinct complex numbers satisfy the equation z^2 + 4z + 4 = 0?
+
What are the solutions to the equation x^2 - 8x + 12 = 0?
+
Question: What is the definite integral of f(x) = 3x^2 - 5x + 2 from x = 1 to x = 4 using the Fundamental Theorem of Calculus?
+
New questions in Mathematics
A normal random variable x has a mean of 50 and a standard deviation of 10. Would it be unusual to see the value x = 0? Explain your answer.
A software company incurs a cost of $50 per license sold plus $5,000 in fixed costs. How many licenses should you sell to minimize total costs?
A normally distributed population has a mean of 118 with a standard deviation of 18. What score separates the lowest 72% of the distribution from the rest of the scores?
(x^2+3x)/(x^2-9)=
Express the following numbers in decimal system, where the subscript indicates the base: 110101 (SUBINDEX=2)
A consulting company charges a fee of $50 per hour for consulting. If their monthly fixed costs are $1,000 and they want to make a monthly profit of $2,500, how many consulting hours should they bill per month?
Derivative of x squared
Subscribers to the FAME magazine revealed the following preferences for three categories: Fashion 30, Athletics 24 and Business 15. Following these frequencies of observation, compute the chi-square test statistic. At the 0.05 level of significance, would you conclude they are similar?
If f(x,y)=6xy^2+3y^3 find (∫3,-2) f(x,y)dx.
(24, -7) is on the terminal arm of an angle in standard position. Determine the exact values of the primary trigonometric functions.
suppose random variable x follows poisson distribution with expected value 3. what is variance of x?
-1%2F2x-4%3D18
Determine a general formula​ (or formulas) for the solution to the following equation.​ Then, determine the specific solutions​ (if any) on the interval [0,2π). cos30=0
16.What payment (deposit) made at the end of each month will accumulate to $10473 in 13 years at 7.9% compounded monthly? Enter to the nearest cent (two decimals). Do not use $ signs or commas in the answer.
A person runs 175 yards per minute write a variable that represents the relationship between time and distance
A block slides across the floor with a force of 20N, which has an angle of 30°. The mass of the block is 2kg and the coefficient of friction is 0.1. Calculate the value of all the forces involved in this system and finally the value of the acceleration.
An election ballot asks voters to select three city judges from a group of 12 candidates. How many ways can this be done?
56 × 12 = 672. How should you adjust this answer 672 to determine 57 × 12? a) The answer increases by 1 b) The answer increases by 57 c) The answer increases by 56 d) The answer increases by 12
The perimeter of a rectangular rug is 42 feet. The width is 9 feet. What is the length?
An export company grants a bonus of $100,000 pesos to distribute among three of its best employees, so that the first receives double the second and the latter receives triple the third. How much did each person receive?