Mathematics College

By using graphical method, find optimal solution of the problem max z = 3x + y s.t 2x - y ≤ 5 -x + 3y ≤ 6 x ≥ 0, y ≥ 0​

Answers

Answer 1

By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Related Questions

Need help on this question pls help!!!!!!!

Answers

The mean is 3 and I don’t know what MAD is, sorry!

Explanation for mean:

There are 15 dots total throughout 5 lines. 15/5=3. For the mean you add up the total number of dots and divide it by the amount of categories.

4y + 3y + 2y =

A. 9y

B. 9y²

C. 9y³

D. 24y

E. none of these

Answers

The answer is 9y since you combine like terms

Answer:

Step-by-step explanation:

Like terms are terms that have the same letter or letters. They can be collected together by adding or subtracting. 9y, 3y and 2y are like terms because they contain the letter y and only the letter y.

4y + 3y + 2y = 9y

a) If 12 quintals of weight is equal to 1200 kg, how many kilograms are there in 1 quintal?​

Answers

1200 kg / 12 quintal

= 100 kg per quintal

so 1 quital = 100 kg

domain of fx=underroot x+2 is equal where {} denotes the fractional part

Answers

The domain of the function f(x) = {√(x + 2)} is x ≥ -2, where {} denotes the fractional part.

To find the domain of the function, we need to consider the values of x for which the expression inside the square root is defined. In this case, the expression x + 2 must be non-negative (since we cannot take the square root of a negative number). So we set x + 2 ≥ 0 and solve for x.

x + 2 ≥ 0

x ≥ -2

Therefore, the domain of the function is x ≥ -2. This means that the function is defined for all real numbers greater than or equal to -2.

In the second paragraph, we explain that the domain of the function f(x) = {√(x + 2)} is x ≥ -2. The function involves taking the square root of (x + 2) and then considering the fractional part of the result.

The expression inside the square root must be non-negative, which means x + 2 ≥ 0. Solving this inequality, we find x ≥ -2. Thus, any real number greater than or equal to -2 is included in the domain of the function.

For example, if we choose x = -2, the expression inside the square root becomes 0, and taking the square root of 0 gives us 0. The fractional part of 0 is also 0. As we move to x > -2, the square root expression becomes positive, resulting in non-zero fractional parts.

So, the function is defined and has a non-zero fractional part for all real numbers greater than -2. However, for x < -2, the expression inside the square root becomes negative, which is not defined in the real number system. Therefore, the domain of the function is x ≥ -2.

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Identify a possible first step using the elimination method to solve the system and then find the solution to the system. 3x - 5y = -2 2x + y = 3 Responses A Multiply first equation by -3 and second equation by 2, solution (1, -1).Multiply first equation by -3 and second equation by 2, solution (1, -1). B Multiply first equation by -2 and second equation by 3, solution (1, -1).Multiply first equation by -2 and second equation by 3, solution (1, -1). C Multiply first equation by -2 and second equation by 3, solution (1, 1).Multiply first equation by -2 and second equation by 3, solution (1, 1). D Multiply first equation by -3 and second equation by 2, solution (-1, 1)

Answers

Answer:

(C) Multiply first equation by -2 and second equation by 3, solution (1, 1)

Step-by-step explanation:

Simultaneous equations:

Simultaneous equations are set of equations which possess a common solution. The equations can be solved by eliminating one of the unknowns by multiplying each of the equations in a way that a common coefficient is obtained in the unknown to be eliminated.

Given the simultaneous equations:

3x - 5y = -2

2x + y = 3

First step:

Multiply first equation by -2 and multiply second equation by 3,

-6x + 10y = 4

6x + 3y = 9

Second step:

Add the two equations together,

13y = 13

Divide both sides by 13

y = 1

Third step:

Put y = 1 in the first equation

3x - 5(1) = -2

3x - 5 = -2

3x = 5 - 2

3x = 3

Divide both sides by 3:

x = 1

solution (x,y) = (1,1)

Option C

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