A local factory uses a manufacturing process in which 70% of the final products meet quality standards and 30% are found to be d
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We have been given a system of inequalities and an objective function.
The inequalities are given as:
And the objective function is given as:
In order to find the minimum value of the objective function at the given feasible region, we need to first graph the region.
The graph of the region is shown below:
From the graph, we can see that corner points of the feasible region are:
(x,y) = (15,30),(30,15) and (30,60).
Now we will evaluate the value of the objective function at each of these corner points and then we will compare which of those values is minimum.
Hence the minimum value of objective function is 975 and it occurs at x = 15 and y = 30
For this case we have the following expression:
The first step is to solve the quadratic term.
We have then:
Then, the second step is to subtract both resulting numbers:
We observe that the result obtained is a negative number.
Answer:
The result of the expression is given by: