Thomas and Theresa work for a company that receives $75 for each unit of output sold. The company has a variable cost of $30 per item and a fixed cost of $12,000.

Based on this information, Thomas and Theresa make some projections about potential profit.

Thomas states that for every 500 units of output sold, the company will make $11,000 in profit.
Theresa states that for every 800 units of output sold, the company will make $24,000 in profit.

Determine a function that models the profit for the company based upon the conditions for revenue and expense.
Are the claims about profit that Thomas and Theresa made true? Explain why Thomas and Theresa are each correct or incorrect and justify your reasoning.

P(x) = 20x - 1600.

Step-by-step explanation:

The revenue of the company is obtained by selling each unit of output for $45.

So. for x units of output sold the revenue will be given by  

R(x) = 45x (1)

Again, the company has the expense of fixed $1600 and another expense of $25 per output of items.

Hence, for x items the cost will be given by  

C(x) = 1600 + 25x

Therefore, the function that models the profit of the company based upon the conditions for revenue and cost will be P(x) = R(x) - C(x)

⇒ P(x) = 45x -(1600 + 25x) = 20x - 1600. (Answer)

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

it would be 6xy and -16xy.