Find the vaules of x and y that maxmize the objective function p= 3x+2y for the graph. what is the maximum value

answer:

step-by-step explanation:

graph the inequalities.

the intersection is known as the ‘feasible’ region.

the ‘corners’ of the feasible region are (0,0), (2,0), (2,2), (0,4), and (1.5,3).

plugging those (x,y) values into the constraint to be maximized:

3(0) + 2(0) = 0

3(0) + 2(4) = 8

3(2) + 2(0) = 6

3(1.5) +2(3) = 10.5   →maximum

3(2) + 2(2) = 10

solution is (1.5, 3)

if the result must contain whole numbers only, then (2, 2)

there is also the 'simplex' method, if that is a topic you have covered.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.