Answer the following Essay Type Questions: (6×3 = 18 marks) Q. 1 An automobile parts manufacturer produces two types of automobile parts used for making four wheelers. Type 1 requires ½ hour of labor and 1 hour of machine time. Type 2 requires 1 hour of labor time and 2 hours of machine time. There are 500 hours available per week of labor and 700 machine hours available. Type 1 has a profit margin of $ 35 a unit and Type 2 have a profit margin of $ 50 a unit. The automobile parts manufacturer must choose the quantity of Type 1 and Type 2 machinery parts, which maximizes profit. Formulate this as a linear programming problem by defining the objective function and the constraints. Solution: Q.2 The Kenneth State organization sells a product for which the annual demand is 5000 units. The average holding cost is $ 1.00 per unit per year, and the ordering cost is $ 100 per order. a) What is the economic order quantity for the product? b) What is the total annual cost for this EOQ? Solution: Q.3 The cost of transportation per unit from three plants (sources) to three retail shops (destinations) are given in table below. Determine the total transportation cost of initial solution using the North-West corner method. To From A B C Requirements D E F Capacity 10 12 9 40 4 5 7 50 11 8 6 60 70 50 30 150 Also formulate this transportation problem as a linear programming problem. Solution: Q.4 Good fellow manufacturers Inc., uses 50,000 loads of lumber per year. A load of lumber costs $250 and the carrying cost is 10 percent of the unit cost. The cost to order is $500 per order and the lead-time is three working days. Assuming 100 working days, determine: (a) The economic order quantity. (b) The reorder point. (C)The number of orders per year. Solution: Q.5 Flemming Accessories produces paper slicers used in offices and in art stores. The minislicer has been one of its popular items: Annual demand is 10,000 units and is constant throughout the year. Flemming produces the minislicers in batches. On average, Flemming can manufacture 100 minislicers per day. Demand for these slicers during the production process is 50 per day. The setup cost for the equipment necessary to produce the minislicers is $100. Carrying costs are $1 per minislicer per year. a) How many minislicers should Flemming manufacture in each batch? (Optimal production quantity) b) How many orders per year are needed with the optimal policy? (Optimal no. of production runs per year.) c) What is the annual set up cost? Solution: Q.6 Consider the material structure tree for item A below: A B(4) D(8) C(5) E(3) D(6) E(7) If 10 units of A are needed, then find the following a. How many units of B are needed? b. How many units of C are needed? c. How many units of D are needed? d. How many units of E are needed? Solution: Answer the following Essay Type Questions: (6×3 = 18 marks) 1. Consider the project with the following estimates for the activity times and precedence relationships: Activity A B C D E F G H Optimistic Time (a) 3 5 2 2 1 3 7 2 Most Pessimistic Likely Time(m) Time (b) 4 5 7 9 3 10 5 8 7 7 5 7 8 9 6 10 Immediate Predecessor(s) ----A B B C, D D, E F Draw the PERT network associated with the activities and calculate expected time and variance corresponding to each activity. Solution: 2. Using the data given in Q.1, answer the following questions: (a) What is the expected duration of the project? (b) What is the project variance? (c) If the deadline of the project is 25 days, what is the probability of finishing the project on time? Solution: 3. The following Table represents a project with known activity times. All times are in weeks. Immediate Predecessor --A B C, D B E, F Activity A B C D E F G Time 4 3 2 7 4 5 4 Construct the network for this problem and determine the earliest start, earliest finish, latest start, latest finish and slack time for each activity. Solution: 4. Calculate the probability of occurrence, cumulative probability and interval of random numbers for the following data, hence complete the table Solution: Demand Frequency 0 1 2 3 4 5 10 30 20 60 40 50 Probability of Cumulative Interval of Random Occurrence Probability Numbers 5. The number of machine breakdowns in a day is 0, 1, or 2, with the probabilities 0.6, 0.3, and 0.1, respectively. The following random numbers have been generated: 13, 10, 02, 18, 31, 19, 32, 85, 31, 94. Use these numbers to generate the number of breakdowns for 10 consecutive days. What proportion of these days had at least one breakdown? Solution: 6. A diaper making company has opened a cloth diaper service. Company is interested in simulating the number of diapers required for a one-year- old. It hopes to use this data to show the cost effectiveness of cloth diapers. The table below shows the number of diapers demanded daily and the cumulative probabilities associated with each level of demand. Daily Demand 3 4 5 6 7 Cumulative Probability 0.10 0.35 𝑥1 0.90 𝑥2 Interval of Random Numbers 01-10 11-35 36-60 61-90 91-00 a. Find the missing values 𝑥1 and 𝑥2 . b. Find the probability of each of daily demand? c. If the random number 35 were generated for a particular day, what would be the simulated demand for that day? Solution: 
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