min √(x) s.t. μ 20 with variable μ Rm. In particular, show that an optimal solution μ* to this program must satisfy T n t=1 j=1 T n P(Rt(*)¹Ã¡) Ai‚j ≤ xi, Vi, ΣΣP (Rt‚j ≥ (µ*)'Aj) (µ*)¹A; = (µ*)¹x. t=1 j=1 (1) (2)
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Derive the Karush-Kuhn-Tucker conditions for this Bid-price policy program (also shown in the image for clarity),
min J˜µT(x)
s.t. µ ≥ 0
with variable µ ∈ ℝ^m. In particular, show that an optimal solution µ* to this program must satisfy the constraints in the image below:
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- suppose the Total Revenue function for a product is given by R(x)=V0•1x+0-2x² (R-4,x--u) a) Find the Rate of change in Tota) Revenue or Morginal Revenue . a) b) Find Margina) Revenue nhen x=4 units are sold and slate nhatitpredicts for the sale of the next unit c) Firid the Actual change in To tol Revenue uhen productm Level is ingeased from 4 to 5 units di Esplainany discreponcy hetncen parls (1) and (c)resuHs mathemohie ally / Graphically d)(i) Find the rate of change of the function f(x) =x + 2/ 1 − 8x with respect to x when x = 1.(ii) The number of units Q of a particular commodity that will be produced with Kthousand dollars of capital expenditure is modeled by Q(K) = 500 K2/3Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure, whereK(t) =2t4 + 3t + 149 / t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be producedat this time?(b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?It is estimated that a grocer’s daily profit from the sale of two brands of cherry juice is given by thefunction:P(x,y) = (x - 30)(70 - 5x + 4y) + (y – 40)(80 + 6x – 7y) centswhere x is the price per can of Brand V Juice and y is the price per can of Brand Triple V Juice. CurrentlyBrand V Juice sells for 50 cents per can and Brand Triple V Juice sells for 52 cents per can.i. Use marginal analysis to estimate the change in the daily profit that will result if the grocer raises theprice of Brand Triple V by one cent per can while keeping the price of Brand V unchanged.ii. Find a stationary point of the daily profit function. Classify this stationary point.
- Q4 A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand,where P(t) =6?2 + 5? /(? + 1)2 production in the long run (i) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture.Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0),but for x > 0,it is found that y =0.5(x2 + 3x)/ x3 + x2 + 4x Required:a)Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?Which one of the following is the derivative of √k? O (1/2)k-1/2 ○ (1/2)k 2k² O Oo(b) A firm manufactures benches and tables: the quantity of benches manufactured is B and the quantity of tables manufactured is T. The total cost of manufacturing benches and tables is given by the equation: Cost = 3B2 + 5T²2 – 2BT. There is a shortage of lumber available to manufacture these items, and so, only 60 items in total have been promised to a customer. (i) Create the Lagrangian expression for Cost. (ii) The Lagrangian equations are given: 6B – 2T – 1 = 0 10T – 2B – A = 0 60 — В - Т%3D0 Calculate the minimum cost possible. (iii) If more lumber now becomes available, what selling price would be required to make a profit on an additional item produced?
- y = (3 - x)6 + 7 apply the function in economic optimization conceptOregon Fiber Board makes roof liners for the automotiveindustry. The manufacturing manager is concerned aboutproduct quality. She suspects that one particular failure, tears in the fabric, is related to production-run size. An assistantgathers the following data from production records: a. Draw a scatter diagram for these data.b. Does there appear to be a relationship between run sizeand percent failures? What implications does this datahave for Oregon Fiber Board’s business?Hi, I have been trying to compute the optimal values from this lagrangian. But I can't seem to find a way to get the values from the answer key. I attached both the question and answers. Could you please explain to me how to get these values from the first-order conditions? Thank you very much
- pols Add-ons Help Last edit was seconds ago xt I UA Calibri 11 + 三 2 | 3 II | I 4 II| II6 4. Thanks to years of consistent contracts and an outstanding administration, Crestwood High School has formed one of the best teaching staffs in the State of Michigan. This staff has learned how to work seamlessly with each other and students. They are now able to effectively teach more students in every class than before. *Name the determinant: Automakers have introduced new heating lamps to their paint shops that allow them to dry layers of paint faster than ever before. These newly invented heaters use less energy and have greatly increased output. 5. *Name the determinant: 27°C Rain II 近Technology B uses 4 workers and 2 tonnes of coal to produce 100 meters of cloth. The worker's wages cost $10 and coal costs $5. We have previously calculated that the total cost of production is $50 and that the vertical intercept of the isocost line is 10.If there was a technology that used 1 more worker, how much would it have to decrease the coal required in order to cost the same? (Note: this is the absolute value of the slope of the isocost line.)2.1 Write a well-commented function program for the function x²e¬ª*, using entry-wise operations (such as .* and .*). To get e" use exp(x). Plot the function on [-5,5] using enough points to make the graph smooth. Turn in the program and the graph.