Refer to Question 18 (Maximum value of Z+ Minimum value of Z) is equal to

The correct answer is -17.

To find the value of (Maximum value of Z + Minimum value of Z), we need to analyze the objective function and the corner points of the feasible region defined in the linear programming problem (LPP).

1. Identify the Objective Function:
The objective function for this problem is:
$$Z=3x-4y$$

2. Identify the Corner Points:
The corner points of the bounded feasible region for the given constraints are:
$(0,0)$, $(5,0)$, $(6,5)$, $(6,8)$, $(4,10)$, and $(0,8)$.

3. Evaluate the Objective Function at Each Corner Point:
We substitute the coordinates of each corner point $(x,y)$ into the objective function $Z=3x-4y$:

• For corner point $(0,0)$:
$$Z=3\left(0\right)-4\left(0\right)=0$$
• For corner point $(5,0)$:
$$Z=3\left(5\right)-4\left(0\right)=15$$
• For corner point $(6,5)$:
$$Z=3\left(6\right)-4\left(5\right)=18-20=-2$$
• For corner point $(6,8)$:
$$Z=3\left(6\right)-4\left(8\right)=18-32=-14$$
• For corner point $(4,10)$:
$$Z=3\left(4\right)-4\left(10\right)=12-40=-28$$
• For corner point $(0,8)$:
$$Z=3\left(0\right)-4\left(8\right)=0-32=-32$$

4. Determine Maximum and Minimum Values:
Comparing all calculated values of Z:
• The Maximum value of Z is 15 (occurring at the corner point $(5,0)$).
• The Minimum value of Z is -32 (occurring at the corner point $(0,8)$).

5. Calculate the Required Sum:
Now, we calculate the sum of the maximum and minimum values of Z:
$$\text{Maximum value of }Z+\text{Minimum value of }Z=15+(-32)$$
Simplifying the expression:
$$15-32=-17$$
Therefore, the sum of the maximum and minimum values of Z is equal to -17.