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Question 629968: I've been trying to do this problem for a while.
2. The Iron Range Steel Company determines that a monthly production
level of 10,000 tons of steel allows for a sell price of $206/ton. Doubling production
results in a price drop to $166/ton. Find the price y in terms of the
number x of tons of steel produced and sold. Assume that the graph of y to
x is linear. How much steel must Iron Range produce if the sell price is set at
$190/ton?
3. Find the revenue function R = xy for the Iron Range Steel Company in
problem 3. Write R in the form: R = ax2 + bx + c.
A. Find the vertex.
B. What is the maximum revenue?
C. How many tons of steel should be produced and sold in order to obtain
maximum revenue?
D. What price should be charged/ton to guarantee that the company earns
maximum revenue?
I found the slope of the line to be -.004 by using 206-166 over -10000 making the linear equation y=-.004x+40 However when i get to trying to find how much steel in terms of 190 per ton im lost.
also i am not sure what to do with #3 in terms of writting it in 
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 2. The Iron Range Steel Company determines that a monthly production
level of 10,000 tons of steel allows for a sell price of $206/ton. Doubling production results in a price drop to $166/ton. Find the price y in terms of the
number x of tons of steel produced and sold. Assume that the graph of y to
x is linear.
You have 2 points relating tons and price: (10,000,206) and (20,000,166)
slope = (166-206)/(10,000)= -40/10,000 = -0.004
Form: y = mx + b
Solve for "b":
206 = -0.004*10000 + b
b = 206 + 40
b = 246
Equation:
y = -0.004*x + 246
========================
How much steel must Iron Range produce if the sell price is set at
$190/ton?
Solve: 190 = -0.004*x + 246
x = 14000 tons
======================================
3. Find the revenue function R = xy for the Iron Range Steel Company in
problem 3. Write R in the form: R = ax2 + bx + c.
R = -0.004x^2 + 246x
----
A. Find the vertex.
Vertex occurs at x = -b/(2a) = -246/(2*-0.004) = 30750
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B. What is the maximum revenue?
R(30750) = $3,700,000
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C. How many tons of steel should be produced and sold in order to obtain
maximum revenue?
Ans: 30,750 tons
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D. What price should be charged/ton to guarantee that the company earns
maximum revenue?
y = -0.004*30750 + 246
y = $123
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Cheers,
Stan H.
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