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Determine all local optimum points and inflection point by using second derivative test. f(X) = X3 – 6X2 + 9X + 1. Sketch the graph.
Q#2: When x gallons of Olive Oil are produced, the average cost per gallon is A(x), where
A(x) = 5000/(0.1X + 25) + 0.30X , X > 0,
- Find the value of x at the local optimum point of A(x).
- Prove that (a) is a
local minimum . - Compute the minimum average cost per gallon.
Q#3: Find the area bounded by the given functions listed below:
f(X) = X2 and g(X) = 2 – X Sketch the graph.
Q#4: A fixed cost of $50 thousand was incurred in setting up an operation. At time t months thereafter, the operation yields income at the rate of (20 – 0.3t) and incurs expenses at the rate of (10 – 0.1t); where both are in thousands of dollars per month. Sketch the graph.
- What is the optimal time to terminate the operation?
- What will total profit be at the optimal time of termination?
Q#5: At market equilibrium, consumers demand 625,000 gallons of kerosene, whose supply function is, Ps(q) = 2.5 + 0.3 q3/2 , where q is in thousands of gallons and Ps(q) is in dollars per gallon. Compute producers’ surplus.
Q#6: The demand function for a product is Pd(q) = 80 / (0.2 q + 1)2 , where q is in millions of tons and Pd (q) is in dollars per ton. Market equilibrium occurs at a demand for 15 million tons. Compute consumers’ surplus.
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