a. Develop a decision analysis formulation of this problem by identifying the decition alternatives, the states of nature, and the payoff table.
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- 19. What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (1) 2x + 3y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x, y ≥ 0. Part 2 A. x = 0, y = 3 B. x = 2, y = 0 C. x = 0, y = 0 D. x = 0, y = 4 E. x = 1, y = 5Jean Clark is the manager of the Midtown Saveway-Grocery Store. She now needs to replenish hersupply of strawberries. Her regular supplier can provide as many cases as she wants. However,because these strawberries already are very ripe, she will need to sell them tomorrow and thendiscard any that remain unsold. Jean estimates that she will be able to sell 12, 13, 14, or 15 casestomorrow. She can purchase the strawberries for $7 per case and sell them for $18 per case. Jeannow needs to decide how many cases to purchase. Jean has checked the store’s records on dailysales of strawberries. On this basis, she estimates that the prior probabilities are 0.1, 0.3, 0.4, and 0.2for being able to sell 12, 13, 14, and 15 cases of strawberries tomorrow. a. Develop a decision analysis formulation of this problem by identifying the decisionalternatives, the states of nature, and the payoff table. b. How many cases of strawberries should Jean purchase if she uses the maximin payoffcriterion? c. How…Exercise 4 a) Write the objective function of this LP.b) Write the constraint of the basic element Y.c) Write the constraint that expresses"the factional contributions from each mine must add up to 1."d) What is the optimal fraction of a ton to be chosen from mine 4?e) To make the optimal fraction of a ton to be chosen from mine 4 non-zero, how should the cost per ton of ore from mine 4 change?f) If the minimum requirement amounts of basic element X increases to 7 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?g) If the minimum requirement amount of basic element Z decreases to 25 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?
- Mary is a sales person for Challenge Furniture. She receives an incremental commission based on the table below. If she sells $26,000 and has already received a draw of $766.15, how much commission is still owed to Mary? level 1 1-11,700 3.7% sales volume 2 11,701-21,200 4.3% commission rate 3 over 21,200 4.7%Item5 Time Remaining 2 hours 52 minutes 12 seconds 02:52:12 eBookReferences Item 5 Time Remaining 2 hours 52 minutes 12 seconds 02:52:12 The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits.What is the constraint for Dominican beans? Multiple Choice 12A + 8B ≤ 4,800. 8A + 4B ≤ 3,200. 8A + 12B ≤ 4,800. 4A + 8B ≤ 3,200. 4A + 8B ≤ 4,800.Problem 2: Comp-Max Computers assembles computers and computer equipment. It is about to start production of threenew types of computers, called model X, Y, and Z, respectively. Each type will require assembly time, inspection time, and storage space. The availability of each of these resources is limited. Specifically, available assembly time is 400 hours, available inspection time is 300 hours, and available storage space is 500 cubic feet (about 14.2 ms). The amount of each resource required for the different products is reported in the table below. Model X earns a profit of $100 per unit, model Yearns a profit of $125 per unit, and model 2 earns a profit of $200 per unit. Due to some prior agreements with customers, Comp-Max must produce at least 12 model X computers. In addition, management requires that the fraction of total production made up of model 2 computers must not exceed 25%. RESOURCE REQUIREMENTS Assembly time Inspection time Storage space MODEL hrs/unit hrsJunit cu.…
- #1- Maxwell Manufacturing makes two models of felt tip marking pens. Requirements and available resources for each lot of pens are given in the following table: Fliptop Model Tiptop Model Available Plastic 3 4 36 Ink Assembly 5 4 40 Molding Time 5 2 30 The profit for either model is $1,000 per lot. a) What is the linear programming model for this problem? b) Using Microsoft Excel's Solver, find the optimal solution. How many Fliptop models and how many Tiptop models should be produced? What is the maximum profit? c) Will there be excess capacity in any resource? Use Excel's Solver and run a sensitivity report to answer the following questions. d) Over which range can the objective function coefficient for Fliptop Models change without affecting the original optimal solution? What is this range called? e) What is the shadow price (dual price) for the plastic constraint and how would you interpret it? f) What is the shadow price (dual price)…Mr Sng is a retiree in his late sixties. He has $100,000 to invest. He has no regular source of income and no other assets. He is evaluating between 3 different lump-sum financial products shown in Table 3. All products require a minimum investment sum of $100,000. Monetary returns represent the net gain after one year of investing in the product. For example, if Mr Sng chose to invest in Product B, he may lose $5,000 after one year if the GDP growth is negative. He will earn $8,000 if the GDP growth exceeds 2% at the end of the year. If you were in the shoes of Mr Sng, how would you select the appropriate investment product for a time horizon of one year? (i) Use the Optimistic, Conservative and Regrets payoff analysis approaches. State which product(s) Mr Sng should invest in and what monetary return he can expect from each approach (ii) As you have only enough funds for one product, identify the most appropriate investment product. [Hint: Be sure to consider the…Problem 6-09 (Algorithmic) The Ace Manufacturing Company has orders for three similar products: Product Order (Units) A 1750 B 500 C 1100 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are as follows: Machine Capacity (Units) 1 1550 2 1450 3 1150 Product Machine A B C 1 $0.80 $1.30 $0.70 2 $1.40 $1.30 $1.50 3 $0.80 $0.80 $1.20 Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". The linear programming formulation and optimal solution are shown. Let xij = Units of…
- Hot Oven daily requirements of 70 g of protein, 1 g calcium, 12 mg iron, and 3000 calories are needed for a balanced diet. The following foods are available for consumption with the cost and nutrients per 100 g as shown. protien (g) calories calcium(g) iron(mg) cost (ghc) brown bread 12.0 246 0.1 3.2 0.5 cheese 24.9 432 0.2 0.3 20 butter 0.1 793 0.03 0.0 1.0 baked beans 6.0 93 0.05 2.3 0.25 spinach 3.0 26 0.1 2.0 0.25 The objective of the Hot Oven is to find a balanced diet with minimum cost.a) Formulate a linear programming model for this problem. b) Use solver to find optimal solution and sensitivity report. c) Management have asked you to determine the optimal solution. Write your answer in a form of a report to be submitted to the management. d) Advice the management about objective function value corresponding to your answer in (b)A wood products firm uses available time at the end of each week to make goods for stock.Currently, two products on the list of items are produced for stock: a chopping board and a knifeholder. Both items require three operations: cutting, gluing, and finishing. The manager of thefirm has collected the following data on these products.TIME PER UNIT (MINUTES)Item Profit/Unit Cutting Gluing FinishingChopping board $2 1.4 5 12Knife holder $6 0.8 13 3The manager has also determined that, during each week, 56 minutes are available for cutting, 650minutes are available for gluing, and 360 minutes are available for finishing.a. Determine the optimal quantities of the decision variables if the goal is to maximize profit.b. Which resources are not completely used by your solution? How much of each resource isunused?8-1 (Production problem) Winkler Furniture manufactures two different types of china cabinets: a French Provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting, and finishing. The table on this page contains all relevant information concerning production times per cabinet produced and production capacities for each operation per day, along with net revenue per unit produced. The firm has a contract with an Indiana distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day). Owner Bob Winkler would like to determine a product mix to maximize his daily revenue. Cabinet Style Carpentry (Hours/Cabinet) Painting (Hours/Cabinet) Finishing (Hours/Cabinet) Net Revenue/Cabinet ($) French Provincial 3 1.5 0.75 28 Danish Modern 2 1 0.75 25 Department Capacity (Hours) 360 200 125 a) Formulate as an LP problem. b) Solve using an LP software program or…