jmoreno486
09.03.2020 •
Mathematics
Consider the following linear programming problem: Max Z = $200x1 + $100x2 Subject to: 8x1 + 5x2 ≤ 80 2x1 + x2 ≤ 100 x1, x2 ≥ 0 What is maximum Z and the value of x1 and x2 at the optimal solution?
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Ответ:
The maximum value of Z is 2,000 for x_1=10 and x_2=0
Step-by-step explanation:
we have
-----> inequality A
-----> inequality B
-----> inequality C
-----> inequality D
Solve the system of inequalities by graphing
The solution is the triangular shaded area
see the attached figure
The vertices of the shaded area are
(0,0),(0,16) and (10,0)
we have
To find out the maximum value of Z, substitute the value of x_1 and the value of x_2 of each vertex and then compare the results
therefore
The maximum value of Z is 2,000 for x_1=10 and x_2=0
Ответ:
The rate of change: 1/5
Initial value: (0,-1)
Step-by-step explanation:
The rate of change is easily 5/25, we just have to simplify it to 1/5.
To get the intial value, just subtract (2,9) by the rate of change twice.