Consider the following model to maximize profit: Max 4x+2y S.T.: 2x+3y>=6 x<=6 y<=8 x,y>=0 The orange dash line below is the objective function (profit line) currently at 30 and the constraints are the red, blue, and green areas. Also take into account the non- negativity constraints. 2x + 3y 26 x≤6 y≤8 4x + 2y = 30 X X X X хххх -10
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- Suppose the outputs of beauty shops and pet-grooming salons are complementary, providing one-stop shopping for personal and pet maintenance. Betty Beehive is thinking about moving her beauty shop from an isolated location to a vacant building next to Peter’s pet grooming shop.In making her decision, she makes the following assumptions: If Betty moves, she will keep all her current customers (20 people per week) and attract 25% of Peter’s current customers. Peter currently has 60 customers per week. 3. Excluding rent, Betty’s profit per beauty treatment is $10. 4.The weekly rent at the new location is $200 higher than Betty’s current rent. Question = If Betty moves her beauty shop, will her profits increase or decrease? By how much? Question =Suppose that if Betty makes the move, 50 percent of her original customerswill switch from George’s grooming salon to Peter’s. If Peter’s profit pertreatment is $8, how much would he be willing to pay Betty to make themove? Will the…1. A) An automobile company sells 2 tires for every one frame. Now the demand function for tire is 3 t=189 - P and demand function for frame f-180 – Pf and firm's cost function is C=3t2 + 3f2 + 3tf + 570 now use the Lagrange Multiplier Method of constrained optimization to optimize the profit. b) Now use the Bordered Hessian method to show that all the optimal values that you find 4 in (a) maximize the profit. c) Define the significance of Lagrange Multiplier in optimization using this context. What is the other name of Lagrange Multiplier? Please briefly discuss how it will affect a firm's decision in this context? (Hint: is there any constant in your constraint?)A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150 - 0.02 x Demand for an annual printing of this particular product. The fixed costs per year (ie., per printing) = $46,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 3,000 units per year. The maximum profit that can be achieved is $. (Round to the nearest dollar.) The unit price at the point of optimal demand is $ per unit. (Round to the nearest cent.) Enter your answer in each of the answer boxes.
- Problem Set: A х —3 (1) For the function f(x)= evaluate and simplify the following: 4- 2x? (i) f(-1) (ii) f(2a–b) (2) The length of a rectangular floor is two metres more than twice its width. If a diagonal of the rectangle is 13 meters, find the area of the floor. (3) The demand function for a tablet is given by the model p= 200 – 16x where p is measured in dollars per tablet and x is measured in millions of tablets. If it costs $50 to produce each tablet and a profit of $125 million was derive when 2.5 million tablets were produced. Derive the number of tablets that the company could sell to make the same amount of profit?A lake has two species of fish: bass and catfish. The number of bass and catfish living in the lake, B and C respectively, depend on the temperature of the lake, T (in degrees Farenheit). The functions modeling this dependency are given below: B(T) = 8T2 + 976T – 28890 С(Т) 3D — 2T?+244T — 6893 What are the two temperatures at which the number of bass in the lake is the same as the number of catfish? Enter exact expressions or round your answers to the nearest thousandth. T : TThe marginal profit for a certain company is MP₁(x) = -x² + 18x-45. The company expects the daily production level to rise from x = 3 to x = 5 units. The management is considering a plan that would have the effect of changing the marginal profit to MP₂(x)= -x² +14x-33. Should the company adopt the plan? Determine the area between the graphs of the two marginal profit functions from x = 3 to x = 5. Interpret this area in economic terms. C Should the company adopt the plan that would make the marginal profit be MP₂? O A. Yes, because the company will make a larger profit under the new plan. B. No, because the company's profit will be smaller under the new plan. O C. It is impossible to tell using the given information. The area between the graphs of the two marginal profit functions from x = 3 to x = 5 is sq. units.
- A stadium can seat 60,000 people. Assume 35% of seats are not occupied (not for sale) because of Covid-19 and social distancing requirements. You are told that the current price of tickets is $70 and that the demand is linear and that the demand function (Qd) = 60,000 - 250P. examine the market for tickets for games at the stadium during these Covid times. You should Illustrate themarket for tickets using a demand and supply diagram. Show all your calculations and properly label the diagram. At $70 a ticket the cap on the number of seats available (because of Covid restrictions) is creating a shortage. How many people miss out on tickets when they are priced at $70 per ticket?Consider the problem: minf,(x, y) = x² +y² minf;(x, y) = y²= x + 5 st. -5 < x, y:<5 Solve by the constraint method: find only a few Pareto optimal: 2: solutionsPLEASE ANSWER D & E You are the manager of a firm that specializes in small single-board widgets. Your goal is to determine the number of units (Z) that must be produced and sold by your firm each month in order to maximize profits. The total benefits (revenues) and costs to your firm of producing various quantities are given in the first three columns of the following table. Based on this scenario, complete the table and answer the accompanying questions: Control Variable Z Total Benefits B(Z) Total Cost C(Z)0 0 01 200 102 380 303 540 604 680 1005 800 1506 900 2107 980 2808…
- The wage rate of Zeta Corp. employees is 20 million per month, while the cost of one unit of machine is 80 million per month. Currently, Zeta Corp. produces 100 units of output and employs 20 employees and uses 5 units of production machines. This combination of factors of production is the most efficient for the company. So If Zeta Corp. wants to increase its output to 200 units but it cannot change its number of machines (from 5 units), what is the optimal number of employees and production costs of Zeta Corp.?The demand function for a tablet is given by the model P= 200-16x2 where p is measured in dollars per tablet and x is measured in millions of tablets. If it costs $50 to produce each tablet and a profit of $125 million was derive when 2.5 million tablets were produced. Derive the number of tablets that the company could sell to make the same amount of profit?What is this equation used for? What do the variables mean? Can you give an example how a research study can be applied to this formula? Does it account for control variables ?