Given that
The objective function is represented as
z = 4x + 6y
And we have to find the maximum and minimum value of the objective function.
Explanation -
The given points on the graph are
A (3, 10)
B (7, 5)
C (8, 3)
D (2, 2)
And we have to find the value of the objective function at A and the maximum and minimum value of the objective function.
So we will find the value of the objective function at all the points.
![\begin{gathered} The\text{ value of objective function at A \lparen3,10\rparen,} \\ z=4*3+6*10=12+60=72 \\ \\ The\text{ value of objective function at B \lparen7,5\rparen,} \\ z=4*7+6*5=28+30=58 \\ \\ The\text{ value of object}\imaginaryI\text{ve funct}\imaginaryI\text{on at C \lparen8,3}\operatorname{\rparen} \\ z=4*8+6*3=32+18=50 \\ \\ The\text{ value of object}\imaginaryI\text{ve funct}\imaginaryI\text{on at D}\operatorname{\lparen}2,2\operatorname{\rparen}\text{,} \\ z=4*2+6*2=8+12=20 \end{gathered}]()
Hence the maximum value of the objective function is at A i.e 72
and the minimum value of the objective function is at D i.e 20.
Final answer -
So the final answer is - The value of the objective function at A is 72.And the maximum and minimum values are 72 and 20 respectively.