Find the maximum value of p=3x+2y subject to the following constraints 5x+y< 16
2x+3y< 22
x> 0
y> 0

The maximum value of p is 18

Step-by-step explanation:

we have

------> constraint A  

----> constraint B

----> constraint C

----> constraint D

using a graphing tool

The solution is the shaded area

see the attached figure

The vertices of the solution area are

(0,0), (0,7.3), (2,6) and (3.2,0)

To find the maximum value of p, substitute the value of x and the value of y of each vertices in the equation and then compare the results

For (0,0)

For (0,7.3)

For (2,6)

For (3.2,0)

therefore

The maximum value of p is 18

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,