Assignment3_ 02122020 copy.docx - Certificate Program in...

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1 Certificate Program in Business Analytics and Intelligence (BATCH 7) Module 4: Prescriptive Analytics Instructions 1. This is a take-home assignment. You are free to discuss the assignment questions with your classmates. However, you are not allowed to copy the answers from other students. 2. Answer all questions; there are 4 questions in this assignment. 3. Show all work and give adequate explanations to earn full credit. The mathematical equations of the solutions should be clearly mentioned, and Outputs must be interpreted and clearly explained. Software outputs without mathematical explanation will NOT be given credits. 4. Codes run in tools need not be shared. Excel/other software outputs alone shall not be treated as complete answers 5. Encircle or underline your final answer for each part. 6. Use significance of 0.5 ( = 0.05) wherever required. 7. Completed assignment should be submitted on Moodle by 5 th January 2021 23.55 Hours. Assignments will not be accepted after 5th January 2021; the grades of such students will be marked Incomplete (I) in the grade sheet and course completion certificate will be detained.
Question 1 (20 points) The ABC Corporation makes two products with brand names ‘Swift’ and ‘Impala’. The net contribution from each product is Rs. 1 and Rs. 2, respectively, measured in lakhs. There are three workshops that are used to make these products. The first one called Tuning (T) has 50 hours a week available. Each Swift requires 1 hour and each Impala 3 hours in the Tuning workshop. The second workshop is called Finisher (F) and has 40 hours available. Each product requires one hour in this workshop. The third workshop is Assembly (A) and has 120 hours available. Swift requires 3 hours and Impala 2 hours in the Assembly workshop. (a) Formulate the above problem as a linear program to determine the number of Swift and Impala products to be manufactured to maximize profit. (3 points) (b) Solve this problem graphically. Show the optimal variable values as well as the optimum objective function value on the graph. (3 points) (c) Write the dual to your LP formulation from part (a). Using the dual formulation, determine the shadow prices of the constraints in the primal problem? (6 points) (d) What change do you expect if the T and A workshop hours are simultaneously increased by 10 hours each? (1 point) (e) Notice that the net profit of the Swift model is half of that of the Impala model. If the profit for Swift is further reduced by Rs. 20,000 (or Rs. 0.2 lakhs), will the company make more Impalas and less Swifts? (2 points) (f) A new product called Gazelle is being considered for production. It yields a much higher net profit of Rs. 3 lakhs per unit, while requiring 3,4, and 5 hours in the Tuning, Finishing and Assembly workshops, respectively. Should the ABC corporation take up production of the

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