The activity times (in months) for the following project network: Activity Time Start A 7 a. Find the critical path. B BCDEFG 8 3 6 3 9 5 C E F Finish b. The project must be completed in 1% years. Do you anticipate difficulty in meeting the deadline? Explain. The critical path activities require months to complete. Thus the project should be completed in years.
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- Problem 4You are the manager of a manufacturing firm, and you are considering purchasing a newmachine for your assembly-line process. The machine costs $105,000. The economists that workfor the company estimate that the additional income from the machine will be a constant $7800for the first year, then will increase by $700 each year after that. In order to buy the machine, thecompany needs to be convinced that it will pay for itself by the end of 8 years with thisadditional income. Money can earn 2.7% per year, compounded continuously. Should thecompany buy the machine? Please provide your analysis to the chief operating officer (COO) ofthe company.Suppose a lottery with 1,000,000 tickets has a first prize of $200,000, three second prizes of $60,000 each and 100 third prizes of $200 each. How much should the state charge for a ticket if it needs 10% of the revenue for overhead and wants to make a $500,000 profit ?Question 3Bob is a young entrepreneur who recently graduated from UPSA and using three different ingredient (flour, sugar and butter) to produce three different kinds cakes namely Boban, Boapp and Bopine to be supplied to a pastries store at Shoprite. In order to produce a dozen cakes of Boban requires 5g each of flour, sugar and butter. Also, producing Boapp requires 15g each of butter and sugar together with 20g of flour while producing Bopine requires 15g each of sugar and flour, and 20g of butter. In any particular day, the company has a total of 17500g, 16000g and 18500g of butter, sugar and flour available respectively.(a) Write three linear equations and hence form a matrix to represent the above problem (b) Determine the number dozens of cakes of each brand of cakes that should be produced from the available raw materials using matrix inversion
- Problem #2. You are the buyer for the nutritional supplement department of a local pharmacy. A number of vendors in your area carry similar lines of organic vitamins. On bottles of organic vitamin C, Brand A offers a list price of $240 per dozen less a 32% trade discount. Brand B offers a similar bottle for a list price of $325 less a 47% trade discount. (a) Which vendor is offering the lower net price? (b) If you order 300 dozen bottles of organic vitamin C, how much money (in $) will be saved by using the lower-priced vendor?Scenario 14.1 — Vidalia OnionsWhen Vidalia onions are ready, the entire 13 county (plus parts of seven other counties) area in Georgia where they are grown is devoted to the harvest, packaging and shipping of this delicacy. The Onion Shack currently purchases 120,000 bags of onions each year at a price of $100 per bag (a bag is ten pounds). Onion Shack has historically purchased in lots of 3000 bags. Transit time and capacity vary as indicated in the table (lead time is 2 days more than transit time). The safety inventory that Onion Shack requires is 30% of lead time demand and the holding cost for a bag is 15% of cost. Carrier Quantity Shipped (cwt) Quantity shipped (bags) Shipping cost ($/cwt) Transit time (days) Mashburn Rail 200+ 2000+ $2.10 5 Sylvia Express 100+ 1000+ $2.35 3 Anita Enterprises 250+ 2500+ $1.35 3 Smith Trucking 250+ 2500+ $1.00 3 Use Scenario 14.1 to determine the inventory holding cost of the Mashburn Rail option if the Onion Shack purchases…In the following situation, should one machine be purchased and operated 24 hours a day, or should three machines be bought and operated 8 hours? The machine cost $ 95000 with an economic life of 10 years. The 24 operation is really only 96% efficiency because of maintenance and repair activities. Labor is paid in full no matter how many hours they work in each shift. First shift operators get $ 10, second shift operators get $ 12, and third shift operators get $ 14 per hour. With regular one-shift production, the company does not pay for lunch so it gets 8 hours’ work for 8 hours’ pay. Since the plan is to work 5 days a week, what action would you take? Discuss your findings.
- QUESTION 4a. The Healthy Food Restaurant operates seven days a week. The daily requirements for staff areestimated as follows, in Table 5 (below):Table 5. Daily requirements for staff at the Healthy Food RestaurantDays Monday Tuesday Wednesday Thursday Friday Saturday SundayBaseRequirements8 9 9 10 11 12 10Each worker is required to work five days per week, and each must have two consecutive days off.You must include Sunday-Monday days off in your solution to this problem. (i) Use the information given above. Provide in a table, the days off that each worker receives.Problem 2-31 (Algorithmic) Consider the following linear program: Min 2A + 3B s.t. A + 3B ≥ 5 A + B ≥ 4 A, B ≥ 0 Select the correct graph that shows the feasible region and the optimal solution for the problem. (i) B A (ii) B A (iii) B A (iv) B A What is the value of the objective function? If required, round your answer to one decimal place.Objective function value: fill in the blank 2Question.1. A manufacturing manufactures two items X1 and X2 which are handled in a machine shop and assembly shop. Item X1 requires 2 hours of work in a machine shop and 4 hours of work in the assembly shop to manufacture while product X2 requires 3 hours of work in the machine shop and 2 hours of work in the assembly shop. In one day, the industry cannot use more than 16 hours of machine shop and 22 hours of assembly shop. It earns a profit of rupees 3 per unit of product X1 and rupees. 4 per unit of product X2. Give a mathematical formulation of the problem as to maximise profit.
- Question 9 options: A company needs to produce 10,000 items during a year. It costs $100 to prepare for each production run and $10 to produce each item. It costs $2 to store each item for a year. If each production run consists of x items, find x so that the total cost of production and storage is minimizedProblem 2: •BIG produces four types of yogurts A, B, C, and D. Each box of yogurt carries protein, sugar, and Fat. The following table provides information about the content of each yogurt box, together with each box's production cost. BIG wants to produce yogurts in such a way that will provide at least 300 grams of protein with minimum production cost. However, BIG also must ensure they provide at most 200 gm of sugar and 200 gm of Fat while providing the required protein. Moreover, BIG has to produce at least one unit of each type of yogurt, and the number of yogurt A produced should not exceed the number of yogurt C produced.Problem 7-41 Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons. Formulate a linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution. If required, round your answers to two decimal places. Let R =…