Decision Science — DU B.Com. (Hons.) Previous Year Question Papers

2. There are five questions in total. 4. Parts of the question have to be attempted together. - 5. All questions have equal marks. A Manufacturing company makes three products, A, B and C, each of which requires three operations as a part of the manufacturing process. The company can sell all of the products it can manufacture but its production capability is limited by the capacity of its operation centres. (18) Additional data concei.ming the company are as follows: Product Manufacturing Requirements (hours/unit) Cost (Rs.) Selling Price(Rs.) (i) Formulate the above problem as LPP and find the optimal product mix by using simplex method. (ii) Write the dual of the above problem, read the optimal solution of the dual and give its economic interpretation. Given below is the simplex table for a maximization type of linear programming problem: Cj BasicVariable 15 12 11 0 0 0 Quantity Answer the following questions with reasons: (i) Complete the table and test whether solution is optimal or' not? If not, find out the optimal solution. (ii) Is the solution feasible? (iii) Is it a case of multiple solutions? If so, show one such solution. (iv) Is the solution degenerate? If yes, which variable is degenerated? (v) Write the optimal product mix and the profit contribution of the above solution. (vi) If the company produces 13 units ofx3, how many units of x] and X2 shall have to be reduced, if any? (vii) What are the shadow prices of three resources? (viii) If the company wishes to expand the production capacity, which of the three departments should be given priority? (ix) If a customer is prepared to pay higher price for product X3, how much should the price be increased so that the company's profit remains unchanged? (x) Write down the objective function of the above problem. 2. The following table summarizes the supply, demand, and cost information for the three factories (S„ S2, S3) shipping goods to three warehouses (D], D_2, D3). Using the cost information given in the following table: (i) Find the initial basic feasible solution using the vogel's Approximation Method. (ii) Find the optimal solution that minimizes the transportation cost (Use MODI method). ToFrom D| D2 D3 Supply A company has five jobs to be done on five machines. Each job must be done on one and only one machine. The cost (in thousands of rupees) of each job on each machine is given in the following table: What are the job assignments which will minimize total cost? What is the total cost? (18) 3. (a) A Car park contains 5 of 10 per hour. cars. The arrival of cars is Poisson at a mean rate The length of time each car spends in the car park is exponential distribution with a mean of 5 hours. How many cars are in the car park on an average? (b) At what average rate must a clerk at a supermarket work in order to ensure a probability of 0.90 that the customer will not wait longer than 12 minutes? It is assumed that there is only one counter at which customer arrive in a