Contribution per unit £600 £500 Three processes are required for the manufacture of these products: Pro Beta and Process Gamma. The processing time (in hours) required for the of each product is as follows: Product MM Product LL Prod
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- Question 1 A company manufactures two types of boxes, corrugated and ordinary cartons. The boxes undergo two major processes: cutting and pinning operations. The profits per unit are $6 and $4 respectively. Each corrugated box requires 2 minutes for cutting and each carton requires 3 minutes for cutting, whereas each corrugated box requires 2 minutes for pinning and each carton requires 1 minute for pinning. The available cutting time is 120 minutes and total pinning time is 60 minutes. Determine the optimum quantities of the two boxes to maximize the profits. a. Formulate a linear programming model that can be used to determine the quantities of the two boxes that should be produced in order to maximize total profit contribution.b. Graph the feasible region.c. Determine the coordinates of each extreme point.Question 4An investor is to purchase one of three types of real estate, as illustrated in Figure below. Theinvestor must decide among an apartment building, an office building, and a warehouse. Thefuture states of nature that will determine how much profit the investor will make are goodeconomic conditions and poor economic conditions. The profits that will result from eachdecision in the event of each state of nature are shown in Table below: a) Find the optimal act using Maxi-Max criteriab) Find the optimal act using Mini-Max criteria c) Find the optimal act using Maxi-Min criteria d) Find the optimal act using Min-Max regret tableQuestion 3 a) The following represents the transportation cost between three warehouses (1, 2, 3) and four markets (A, B, C, D): The following represents the transportation cost between three warehouses (1, 2, 3) and four markets (A, B, C, D): From Warehouse To Market Supply A B C D 1 14 24 18 28 48 2 17 18 25 16 56 3 30 16 22 30 32 Demand 41 34 35 20 b) Draw a well annotated source destination chart illustrating the LP problem above c) Using systematic nomenclature for the variables, write out an LP formulation for the problem. Please explain how you arrive at the answer and show the different steps to answer them
- Question 1 A A company manufactures two types of boxes, corrugated and ordinary cartons. The boxes undergo two major processes: cutting and pinning operations. The profits per unit are $6 and $4 respectively. Each corrugated box requires 2 minutes for cutting and each carton requires 3 minutesfor cutting, whereas each corrugated box requires 2 minutes for pinning and each carton requires 1 minute for pinning. The available cutting time is 120 minutes and total pinning time is 60 minutes. Determine the optimum quantities of the two boxes to maximize the profits. a. Formulate a linear programming model that can be used to determine the quantities of the two boxes that should be produced in order to maximize total profit contribution b. Graph the feasible region. c. Determine the coordinates of each extreme point. d. What is the optimal solution. e. Solve in excel.Question 1The Rotary Club is holding a pizza sale to finance outreach projects. The Club made an agreement to purchase pizza from Pizza Hut at a 30% discount which the Rotary Club can then resell for a profit. It is expected that of the 500 families in the community, at most 70% will buy pizza. Based on a survey of their personal preferences, the students believe that they should orderno more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. They also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. The standard price (before discount) for the cheese, pepperoni and vegetarian is $12, $15 and $14, respectively. The Rotary Club makes a profit of 10%, 15% and 20%, respectively, for each cheese, pepperoni, and vegetarian pizza they resell. a) Formulate a linear programming model that would determine the optimal solution. An explanation for the derivation of EACH equation should…QUESTION ONEIn August 2020 government through the Republican President, Zambia launched a K470 million Multi sectoral youth empowerment programme. The Head of State said during the launch in Ndola that government will listen more to young people and address their concerns. As a result of this initiative government had identified oil refining as a major business which youths can venture into. Data collected from Indeni oil refinery (specimen) shows that there are two blending processes of which the inputs and outputs per production run are as follows Inputs Outputs Crude A Crude B Petrol Kerosene Process 1 53 58 Process 2 45 44 The maximum amount available of crude A and B is 200 units and 150 units respectively.Market requirements show that at least 100 units of Petrol and 80 units of Kerosenemust be produced. The profits per production run from process 1 and 2 are $3 and $4respectively. You have been hired as a consultant to help these youth groups makerefining a…
- QUESTION THREEGiven the LP below:a) Solve the problem using big M-methodMinimize Z = 3X1 +4X2s.t 4X1 + X2 ≥ 30−X1 − 4X2 ≤ −184X1 + 3X2 ≥ 28X1, X2, ≥ 0Question 1 You may produce seven products by consuming three materials. The unit sales price and material consumption of each product are listed in Table 1. For each day, the supply of these three materials are limited. The supply limits are listed in Table 2. For each day, you need to determine the production quantity for each product. Product Price Material 1 Material 2 Material 3 1 100 0 3 10 2 120 5 10 10 3 135 5 3 9 4 90 4 6 3 5 125 8 2 8 6 110 5 2 10 7 105 3 2 7 Table 1: Product information for Problem 1 Material Supply limit 1 100 2 150 3 200 Table 2: Material information for Problem 1 Formulate a linear integer program that generates a feasible production plan to maximize the total profit (which is also the total revenue, as there is no cost in this problem). Then write a computer program…Question #4 - Jerry Smith is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on 50-mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. The profits will depend on the size of the shop and whether the market is favorable or unfavorable for his products. Because there will be a 5-year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry is also thinking about hiring his old marketing professor to conduct a marketing research study. If the study is conducted, the study could be favorable (i.e., predicting a favorable market) or unfavorable (i.e., predicting an unfavorable market). Develop a decision tree for Jerry.
- Question 1. Busch Gardens Sweets is preparing for the Halloween rush. They prepare two sizes of Peanut/Raisin Ghoulish Delight and need to calculate how many bags of deluxe and standard mixes they can produce. • The deluxe mix takes 0.9 of a pound of raisins and 0.4 of a pound of peanuts.• The standard mix takes 0.7 of a pound of raisins and 0.6 of a pound of peanuts.The shop has 100 pounds of raisins and 70 pounds of peanuts. The profit on the deluxe mix is $1.80 and the standard mix profit is $1.60. The owner wants no more than 110 bags of each type prepared. Do not forget the non-negativity constraint and remember that you cannot sell partial bags (whole numbers only). Use Excel Solver Question 2. Take a screenshot (snip tool) of you excel spreadsheet and save it.Question 3: A catering company must have the following number of clean napkins available at the beginning of each of the next four days: day 1: 15, day 2: 12, day 3: 18, and day 4: 6. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs $0.10 per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs $0.06 per napkin, and a napkin cleaned via slow service is available two days after they were last used. New napkins can be purchased for a cost of $0.20 per napkin. Part A: Formulate the problem as a minimum cost transportation problem. Part B: Use Excel Solver to solve the problem (provide exact values for all variables and the optimal objective function).Question 1 Broad Topic: Sporting Equipment Narrowed Topic: Classification of Protective Gear in Contact Sports. Broad Topic: Farming Tools Narrowed Topic: Classification of Hand Tools in Organic Farming Practices Question 2 Broad Topic: Sporting Equipment Narrowed Topic: Classification of Protective Gear in Contact Sports. Thesis Statement: Through a classification approach, the analysis of protective gear in contact sports reveals distinct categories based on function, material composition, and design, highlighting the essential role these specialized equipment play in safeguarding athletes and minimizing the risk of injuries in physically demanding competitive environments. Question 3. Broad Topic: Sporting Equipment Narrowed Topic: Classification of Protective Gear in Contact Sports. Thesis Statement: Through a classification approach, the analysis of protective gear in contact sports reveals distinct categories based on function, material composition,…