OPRE 6302 on 20 March 2008 - The University of Texas at Dallas

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15. In a single server queue, both the activity and interarrival times are exponentially distributed. The average activity time is 4 minutes and the expected waiting time in the queue is 12 minutes, what is the utilization of the server? (a) Utilization cannot be found without CVa and CVp (b) Utilization cannot be found without the expected interarrival time (c) 50% (d) 66% (e) 75% E u/(1 − u) = Tq/p = 3
Q3. RichChick is an east-Richardson company that produces two types of Chicken cutlets for sale to supermarkets. Cutlets are called Silverlet and Brownlet. Each cutlet consists of white meat and dark meat. Silverlet sells for $12/kg and must consist of at least 80% white meat. Brownlet sells for $10/kg and must consist of at least 40% white meat. At most 300 kg of Silverlet and 500 kg of Brownlet can be sold in the next month. Three types of chicken are used to manufacture the cutlets: Farm-grown chicken, Free Range chicken and Organic-fed chicken. Each chicken’s cost, and its dark and white meat yield are below: Chicken type Farm-grown Free-Range Organic-fed Cost in $ 6 7 8 White meat yield in kg 1 2 2 Dark meat yield in kg 2 1 1 [4pts] a) To formulate a LP to maximize RichChick’s profit in the next month, define decision variables. ANSWER: F, R, O: Number of Farm-grown, free-Range, Organic-fed chicken purchased. DS, DB: Kilograms of Dark meat used in Silverlet, Brownlet. WS, WB: Kilograms of White meat used in Silverlet, Brownlet. [4pts] b) Profit is revenue minus costs, express RichChick’s profit in terms of decision variables. ANSWER: Max 12(WS + DS) + 10(WB + DB) − 6F − 7R − 8O [4pts] c) Write constraints so that RichChick does not attempt to sell more cutlets than next month’s demand. ANSWER: WS + DS ≤ 300 and WB + DB ≤ 500 [4pts] d) Write constraints so that RichChick does not attempt to use more white or dark meat than it buys in the form of Farm-grown chicken, Free Range chicken and Organic-fed chicken. ANSWER: WS + WB ≤ F + 2R + 2O and DS + DB ≤ 2F + R + O [4pts] e) Finish your formulation by adding any constraints you find necessary. ANSWER: Silverlet must have at leat 80% white meat: Brownlet must have at least 40% white meat: WS WS + DS WB WB + DB Nonnegativity constraints: F, R, O, WS, DS, WB, DB ≥ 0 ≥ 0.8. ≥ 0.6.
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OPRE 6302 on 20 March 2008 - The University of Texas at Dallas

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