A. → Use Hessian Matrix to classify the stationary point of the function - π = 50Q₁-20 +9502-40²-3Q1Q₂¶ B. → Write down the associated Hessian-matrix and hence determine the nature of. the stationary point of this function- Z = X² + y² - 2X - 4Y + 15
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- With respect to a given product, describe the connection that exists between equalibrium/disequalibrium and prediction. cite an unique exampleThe demand function for a product is given by P = 4000/ln (x+10), where P is the price per unit in dollars when x units are demanded.i. Find the rate of change of price with respect to the number of units sold when 40 units are sold ii. Find the rate of change of price with respect to the number of units sold when 90 units are sold.iii. Find the second derivative to see whether the rate at which the price is changing at 40 units is increasing or decreasing.Consider the Lagrangian function L=qq, *+2(Y-p,9,- P292) . Which of the following expressions is NOT a first-order condiction of this function: OA (1-a)a;aª-àp2 = 0 O B. aq'a¯ -ap, = 0 OC. (Y-P191 -P292)=0 OD. (1-a)a,a-p2 = 0 Reactic tv MacBook Air 80 DII DD F1 F2 F3 F5 F7 FR F9 F10 F11 ! #3 $ & 1 2 7 8. 9. Q W Y U { H J C V tion command command option V * 00 N Al
- Derive the MU function from the following TU function: ?? = 200? − 25?2 + ?3The first order, and the second order, partial derivatives of the following function are, respectively z = r°y² + 15ye* Select one: = 2r*y O a. 2x3 + 15e" and Ob. 3x + 15e* and 2x * = 2y + 15e" and = 2x Oc. Od. = 2x®y+ 15e* and * = 3.x?y+ 15e" and 6ry e. Clear my choicepotter makes and sells ceramic bowls. It is observed that when the price is $32, only 9 bowls are sold in a week; but when the price decreases to $10, weekly sales rise to 20. Assuming that demand can be modelled by a linear function, (a) obtain a formula for Pin terms of Q (b) Calculate for the slope of the curve if the relationship between p and Q is linear. (c) comment on the likely reliability of the model
- X(t) is a wide sense stationary stochastic process with autocorrelation function sin(271000r) R„(T)=10- 271000r The process Y(t) is a version of X(t) delayed by 50 micro seconds. {Y(t) = X(t - t0)} (a) Derive the autocorrelation function of Y (t). (b) Derive the cross-correlation function of X(t) and Y (t). (c) Are X(t) and Y (t) jointly wide sense stationary? IUnloaded File DetailsHello. May I ask how did you get the values? Were those only assumed values? Can you also explain how did you make the normal form thoroughly?Windies Cricket manufactures Windies supporter jerseys. The quantity q, of thesejerseys demanded weekly is related to the wholesale price per jersey p, by thefollowing equation:? = −0.006? + 15The weekly total cost incurred by Windies Cricket for producing q jerseys is:?(?) = 38? − 0.02?2 + 30,000a. Determine an expression to represent the weekly Revenue functionb. Determine an expression to represent the weekly Profit function.c. Calculate the weekly Revenue when ten dozen jerseys are produced and sold.d. Will Windies Cricket record a loss or profit if they were to produce and sell 2450jerseys?e. If Windies Cricket wishes to maintain a total cost less than $42,000.00, whatrange(s) of Windies jerseys should be produced. f. Calculate the equilibrium price and quantity for Windies jerseys.
- Take the derivatives of the following functions. Do NOT simplify. f(x) = 20x^3 f(x) = 15x + 20x^2 state the limitations of using a cubic function with inflection point to model the side of a hill. What assumptions have been made that may affect the reasonableness of your solutions?Solve the following LPP Max Z = 8 X1 + 10 X2 + 12 X3 X1 + X2> = 22 X1 - X2 = N - 24 X2, Where N is your Number=80 X1, X2, X3> = 0 If the question can be solved by using the graphical method if it can be solved by graphical method find the value of the variables with the objective function. And if it is not possible, explain the reason and suggest a method of solution. Write below your final results or the conclusions you reach