The graph represents the feasible region for the system: y< =2x  x + y< =45 x < =30 minimize the objective function p = 25x + 20y. the minimum value =? and occurs when x = ? and y = ?

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

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.