a) Solve the LP model using the graphical method and determine the optimal solution. b) Calculate slack/surplus for each constraint. c) If the RHS of constraint 1 increases by 1, by how much would the objective function value change? d) If the RHS of constraint 2 increases by 1, by how much would the objective function value change?
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- Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.what is the shawdow price of constraint 1?
- Discuss the five (5) steps of the Theory of Constraints and apply each to asimulation/assumption of a constraint impacting Jaguar.Variable Cells Model Variable W M Constraints Constraint Number 1 2 3 Name Westem Foods Salsa Mexico City Salsa Name Whole tomatoes Tomato sauce Tomato paste Final Value 560.000 240.000 Reduced Objective Cost Coefficient 0.000 1.000 0.000 1.250 Shadow Price Final Value 4480,000 1920,000 1600,000 0.188 0.125 0,000 Constraint R.H. Side 4480.000 2080.000 1600,000 Allowable Increase 0.250 0.150 Allowable Increase 1120.000 1E+30 40,000 Allowable Decrease 0.107 0.250 Allowable Decrease 160.000 160,000 320.000 Analyze the sensitivity report shown above- a. What is the optimal solution and what are the optimal production quantities? b. Specify the objective coefficient ranges. c. What are the shadow prices for each constraint? Interpret each. d. Identify each of the right-hand-side rangesSIMPLEX METHOD A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftsman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. If the profit on a racket and on a bat is Php 20.00 and Php 10.00 respectively, find the maximum profit of the factory when it works at full capacity.
- Define the term constraint.Explain why satisficing exists and why someone would not require an optimal solution.Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. Letting R = number of regular gloves C number of catcher's mitts - leads to the following formulation: Max 5R + 7℃ s.t. 3 R + -C ≤ 1,000 2 -R + -C ≤ 300 3 -R + -C ≤ 100 4 R, C ≥ 0 The computer solution is shown below. Variable R с Optimal Objective Value = 3550.00000 Constraint 1 2 3 Variable R C Cutting and sewing Value 500.00000 150.00000 Finishing Packaging and shipping Reduced Cost 0.00000 0.00000 Slack/Surplus 275.00000 0.00000 0.00000 5.00000 7.00000 Dual Value 0.00000 4.50000 22.00000 Objective Allowable Coefficient Increase 5.50000 3.00000 Allowable Decrease 1.50000 3.66667
- Don't solve. Please give- Decision Variable Constraint Objective functionvariables $E$11 47000 0 35 7.0000001 8.0000001 BO Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$16 LHS 55000 41 55000 10500 47000 $B$17 LHS 72000 35 72000 10500 47000 $B$18 LHS 80000 -8 80000 47000 10500 10500 $B$19 LHS 47000 0 57500 1E+30 The answers to the questions are found in this sensitivity report. Questions: Write your responses in the space provided 1. What is the range of optimality for the BN and BO variables? write your answers in this format: Lower limit <= Coefficient of BN <= Upper limit. Example 22 <= C of BN <= 40 2. What is the range of feasibility for the constraints located on B17 and B18? 3. If the right-hand side of the constraint located on B17 is decreased by 200, what is the effect on the value of the objective function?Problems LU - 2 Wally Beaver won a lottery and will receive a check for $2,500 at the beginning of each 6 months for the next 6 years. If Wally deposits each check into an account that pays 6%, how much will he have at the end of the 6 years?