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- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? A. Product_2 B. Product_1 C. Product_3 Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 13 5 $B$3 Product_2 175 0 25 8 9 $B$4 Product_3 0 −1.5 25 11 3 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 11 4 $B$3 Product_2 175 0 25 12 14 $B$4 Product_3 0 −1.5 25 8 5 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 multiple choice Product_1 Product_2 Product_3
- Only Construct Linear Programming Model for the following Problemb; An individual wishes to invest $9000 over the next year in two typar of inventrent linvestment A yinlds 5% and invertment � yields 8%. Market retearch rocotnenends an allocs tion of at least 25% in A and at most 30% in �. Motsover, investment in A should be at least ball the invertmeut in �. How should the fund be allocated to the two imetrinents?Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 10 5 $B$3 Product_2 175 0 25 10 14 $B$4 Product_3 0 −1.5 25 8 6 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 Choose the product Product 1 Product 2 Product 32. A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal is to maximize profit, what would be the appropriate objective function? Select one: a. Maximize profit Z = $10Y + $25Z b. Maximize profit Z = 0.25Y + 0.20Z c. Maximize profit Z = $40Y + $25Z d. Maximize profit Z = $50(Y + Z) e. Maximize profit Z = $30Y + $20Z
- Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.4 Sunco processes oil into aviation fuel and heating oil. Itcosts $40 to purchase each 1,000 barrels of oil, which isthen distilled and yields 500 barrels of aviation fuel and 500barrels of heating oil. Output from the distillation may besold directly or processed in the catalytic cracker. If soldafter distillation without further processing, aviation fuelsells for $60 per 1,000 barrels, and heating oil sells for $40per 1,000 barrels. It takes 1 hour to process 1,000 barrels ofaviation fuel in the catalytic cracker, and these 1,000 barrelscan be sold for $130. It takes 45 minutes to process 1,000barrels of heating oil in the cracker, and these 1,000 barrelscan be sold for $90. Each day, at most 20,000 barrels of oilcan be purchased, and 8 hours of cracker time are available.Formulate an LP to maximize Sunco’s profits.1. Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you? 2. Suppose that a manager has a choice between the following two mathematical models of a given situation: (a)a relatively simple model that is a reasonable approximation of the real situation, and (b)a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?
- b) Maximize Z = −40X1 −100X2s.t 10X1 + 5X2 ≤ 2502X1 + 5X2 ≤ 1002X1 + 3X2 ≤ 90X1, X2 ≥ 0Solve by simplex method, what are the solutions? Show that this problem hasmultiple solutions and find the solutions?2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, Provident developed…Ariel holds a $10,000 portfolio that consists of four stocks. Her investment in each stock, as well as each stock’s beta, is listed in the following table: Stock Investment Beta Standard Deviation Andalusian Limited (AL) $3,500 0.80 15.00% Kulatsu Motors Co. (KMC) $2,000 1.50 12.00% Western Gas & Electric Co. (WGC) $1,500 1.20 16.00% Makissi Corp. (MC) $3,000 0.50 22.50% Suppose all stocks in Ariel’s portfolio were equally weighted. Which of these stocks would contribute the least market risk to the portfolio? Makissi Corp. Andalusian Limited Western Gas & Electric Co. Kulatsu Motors Co. Suppose all stocks in the portfolio were equally weighted. Which of these stocks would have the least amount of standalone risk? Western Gas & Electric Co. Makissi Corp. Andalusian Limited Kulatsu Motors Co. If the risk-free rate is 4% and the market risk premium is 6%, what is Ariel’s…