Answer the questions concerning the following linear programming problem: a. graph the region bounded by y ≤-2x+6,y≤-1/2 x+3,y≥0,x≥0 b. if the objective function is (x, y)=3x+y , find the maximum value for the linear programming problem. explain

Part a.

On the same xy axis coordinate system, graph the four inequalities. Each inequality divides the xy plane in two parts (shaded region vs unshaded region). The four shaded regions overlap to form what you see in the attached image below (figure 1).

To graph any of the inequalities, you graph the boundary line first which is simply a line through 2 points. Once you have the boundary formed, you'll shade either above or below depending on the inequality sign. Shade above if you have a "greater than" sign; shade below if you have a "less than" sign.

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Part b.

From part (a) earlier, we see that the four vertex corner points are:

P = (0,3)

Q = (2,2)

R = (3,0)

S = (0,0)

Now plug each of those points  into z = 3x+y to see what the largest z value we can get. Check out figure 2 (also attached below) to see the work shown for this part. In that image, we see that z = 9 is the largest z value possible. so this is the final answer for part b since the other values were z = 3, z = 8, z = 0. This value results from plugging in (x,y) = (2,2).

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.