(10 marks) Q3: Use the Finite-Difference method with h = 0.5 to approximate the solution to the boundary-value problem y=-(y)-y+ Inx, 1 ≤x≤2, y(1) = 0, y(2) = In 2 Compute the percentage relative error if the exact solution is y(x) = In x.
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- How are the absolute maximum and minimum similar to and different from the local extrema?f(-3)=The profit function for an operation is given byP(x, y) = 2200 + 24x − x^2 + 80y − y^2where x is the cost of a unit of labor and y the cost of one item. Find the maximum amount of profit that can be generated from this operation. It is necessryto do a prospective analysis of the profitability of this operation. Determine theapproximate increase or decrease in profit if the units of labor increases from 12to 13 while the price of an item remains the same at 40. Also, what if the laborremains steady at 12 but the price increase from 40 to 41?
- Samsung′s total revenue curve is R(q) = 126q + 40q2and its average cost isA(q) = q2 + 12q − 1233 −6930/q.a. State the name of the function derived when the average cost, A(q), andSamsung’s quantity, q, are multiplied.The marginal cost and marginal revenue of a company are MC (q) = 0.03q² − 1.5q + 35 and MR(q) 25, where q is the number of items manufactured. To increase profits, should the company increase or decrease production from each of the following levels? (a) 25 items: The company should production. (b) 50 items: The company should (c) 80 items: The company should production. production. =Find the critical points of f(x) = x³ - 3x² - 24x. %3D
- Find the values of x, y and z that correspond to the critical point of the function: z = f(x, y) = 3x² + 8x - 7y +5y² + 7xy Enter your answer as a decimal number, or a calculation (like 22/7). (Round to 4 decimal places) x= -11.7273 y= 8.9091 Z= Question Help: Video Submit Question (Round to 4 decimal places) (Round to 4 decimal places) Search W FB2. (a) Let X ~ Exp(A). Show that P(X > x + y | X > y) = P(X > x). (b) The result proved in part (a) is called the "memoryless property". Why do you think it's called that? (c) When you get to certain bus stop, the average amount of time you have to wait for a bus to arrive is 20 minutes. Specifically, the time until the next bus arrives is modelled as an exponential distribution with expectation 1/λ = 20 minutes. Suppose you have already been waiting at the bus stop for 15 minutes. What is the expected further amount of time you still have to wait for a bus to arrive?Maximize f = 7x₁ + 6x2 + 10x3 subject to 4x1 + 5x2 + 3x3 18 2x1 + 3x2 + x3 < 3 x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0 If no solutions exist enter DNE in all answerboxes. x1 = x2 = x3 = f = DOUT
- HelpThe production function for a firm is p(x, y) = 72x 3/4 1/4 y where x and y are the number of units of labor and capital utilized. Suppose that labor costs $108 per unit and capital costs $576 per unit and that the firm decides to produce 9216 units of goods. Determine the following. 3/4 1/4 (a) Determine the amounts of labor and capital that should be utilized in order to minimize the cost. That is, find the values of x and y that minimize 108x + 576y, subject to the constraint 9216 – 72x y = 0. X = y = |(Type exact answers in simplified form.)The marginal cost to produce one additional (generic consumer good) after having produced a of them already is modeled by C(x) = 3x² 120x + 4800. How many (generic consumer good)s should a company produce to minimize the marginal cost?
