Jody is working two jobs, one as a carpenter and one as a website designer. He can work at most 50 hours per week and makes $35 per hour as a carpenters and $75 an hour as a website designer. He wants to make at least $2350 per week but also wants to work at least 10 hours per week as a carpenter. Let c represent the
hours he works as a carpenter and let w represent the hours he works as a website designer.
What is the maximum amount of money that Jody can make in a week given the system in.

The maximum amount of money that Jody can make in a week is $3350.

Given that,

He can work at most 50 hours per week and makes $35 per hour as a carpenter and $75 an hour as a website designer.

He wants to make at least $2350 per week but also wants to work at least 10 hours per week as a carpenter.  

We have to find,

What is the maximum amount of money that Jody can make in a week given the system?

According to the question,

Let c represent the  hours he works as a carpenter,

and w represents the hours he works as a website designer.

As a carpenter, he earns $35 per hours

As for web design, he earns $75 per hour.

He wants to work as a carpenter at least 10h in a week and he works 50h per week. So for a maximum, he works as a web designer,

50 - 10 = 40 hours.

Then,

The hours he works as a carpenter c = 10,

And the hours he works as a website designer w = 40

He can work at most 50 hours per week and makes $35 per hour as a carpenter and $75 an hour as a website designer.

Therefore, the equation is,

Hence, The maximum amount of money that Jody can make in a week is $3350.

For more details refer to the link.

link

The maximum is 3350$

Step-by-step explanation:

As carpenter he earns 35$ per hours

As web design he earns 75$ per hours.

We know that 75>35, so for maximum earning he need to work as web designer more.

He wants to vork as a carpenter at least 10h in week and he worls 50h per week. So for a maximum he works as web designer 50-10=40 hours.

So c=10 and w=40

The equation is:

35c+75w=35*10+75*40=350+3000=3350$

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!