E// This table is the solution of the problem Find the optimal solution and Modified that is to find optimal solutions using the stepping stone method?
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- STAR Co. provides paper to smaller companies whose volumes are not large enough to warran paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The cutting patterns have been established: 1 2 Pattern 12ft. 15ft. 30ft. Trim Loss 0 4 1 10 ft. 3 0 7 ft. 8 0 0 4 ft. 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99 hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. hand will be sold on the open market at the selling price. No inventory is held. Number of: 3Suppose your total benefits of renting x DVD's next month is: -²2² +14x+50 The cost of renting a DVD is $2, and so the total cost of renting x DVD's is $2x. Calculate your net benefit from watching 1, 2...8 DVDs. Complete column (2). (Enter your responses as integers.) (1) DVDs Rented 0 1 N345678 2 (2) Total Net BenefitThe person says that 2173 is a prime number because it ends in the number3, and since 3 is a prime number then that means that 2173 is a prime number. Is2173 a prime number? What can you conclude about this person’s reasoning? Explain your answer.
- The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem. X1 X2 S1 S2 S3 1 6. 1. 10 4 1 28 1. 6. -2 -1 The maximum is when x, = x2 = s, = 52 =and sa = n (Type integers or simplified fractions.) %3D tsDetermine the pivot element in the simplex tableau. (If there is more than one correct pivot element, choose the element with the smaller row number.) X1 X2 X3 S1 S2 3 4 2 1 15 1 20 -8 -3 10 1 row column N O O2 Vidhya Balan is planning to liquidate her investments inmutual funds and invest in real estate. Before makingthe change to her investment strategy, Vidhya wants toforecast the price of mutual funds for the next 2 months.She has collected the following data on the average fundprices for the past 10 months.Month Average Fund Price1 55.12 53.83 53.44 52.955 52.156 52.757 52.658 51.59 52.2510 51.7a Using a five-period moving average, forecast theaverage fund price for Period 11.b. Using exponential smoothing with α = 0.3 forecastthe average fund price for Period 11. Assume an initialforecast for Month 2 (F2) as 55.10
- Martin owns an older home, which requires minor renovations. However, the neighborhood where Martin lives mostly includes newly constructed luxury homes. Why might Martin's home increase in value? Based on the principle of substitution, the value of Martin's house will equal the value of the newly constructed homes in the neighborhood. ○ The value of Martin's home will decrease due to the new competition in the neighborhood. Based on the principle of regression, the newly constructed homes in the neighborhood will increase the home values of the entire neighborhood. Based on the principle of progression, the newly constructed homes in the neighborhood will increase the home values of the entire neighborhood.Yearly oil production in Mexico, and yearly oil imports of the US from Mexico can be represented by the functions: P(t) = 3.0 – 0.13t million barrels I(t) 1.4 + 0.06t million barrels in year t, where t is the time in years since the start of 2000. a) What is represented by the functions P(t) – I(t) and I(t)/P(t)? What are the units for these functions? b) Let q(t) = I(t)/P(t). Compute q'(t) and q'(3). Interpret in a complete sentence. c) In marginal analysis, we would use q' (3) to estimate what quantity? Compute the actual value of that quantity and compare it with q'(3).Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis' risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3. The higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $300,000 be invested in the money market fund. Refer to the computer solution shown below. Optimal…
- Suppose that Pizza King and Noble Greek stopadvertising but must determine the price they will chargefor each pizza sold. Pizza King believes that Noble Greek’sprice is a random variable D having the following massfunction: P(D $6) .25, P(D $8) .50, P(D $10) .25. If Pizza King charges a price p1 and NobleGreek charges a price p2, Pizza King will sell 10025( p2 p1) pizzas. It costs Pizza King $4 to make a pizza.Pizza King is considering charging $5, $6, $7, $8, or $9 fora pizza. Use each decision criterion of this section todetermine the price that Pizza King should charge.max TR = 8x1 + 10x2 subject to 0.5x; s0 8x: s 32 5x: 2 10 X 20 G-1, 2) - XI + 4x, + Calculate the primal problem solution. You are to provide numeric values for the xj, s, and TR.Q1. Build a linear programming model to develop an investment portfolio that minimizes total risk under the above constraints. a) Define the decision making variables. b) Show the objective function. c) Show the constraints. Q2. What is the optimal solution and what is the value of the objective function? Show the relevant portion of the Solver’s output. Fully interpret the results. Q3. What are the objective coefficient ranges for the four stocks? Show the relevant portion of the Solver’s output. Fully interpret these ranges. Q4. Suppose the investor decides that the annual rate of return no longer has to be at least 9% and agrees to at minimum level of 8%. What does the shadow price associated with this constraint indicate about a possible change in total risk that could occur from this lower rate of return? Show the relevant portion of the Solver’s output. Fully interpret the results.