Maximize the product of a and b is 2a+3b=6

a = 3.9 and b r - 5.5

Step-by-step explanation:

2a+3b=6

Let's write this in the form of b = (Solve for b).

3b+6 = 2a

3b = 2a - 6

b = (2a - 6) / 3

b = 2/3a - 1/2

Now substitute this in the original equation.

2a+3b=6

b = 2/3a - 1/2

2a + 2 (2/3a - 1/2) - 12

2a + 4/3a - 1 - 12

Try to write a in terms of thirds. So use 2a = 6/3a

6/3a + 4/3a - 1 - 12

10/3a - 13

Solve for a means write in the form of a =

10/3a - 13

10/3a = 13

multiply both sides with 3/10

3/10 * 10/3a =. 3/10 * 13

30/30 a = 39/10

a = 39/10

Now substitute a = 39/10 in b = 2/3a - 1/2

b = 2/3a - 1/2

a = 39/10

b = 2/3 * 39/10 - 12

b = 78/30 - 12

b = - 5.5