Question 629968
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

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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
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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
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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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