PFA

PFA


KINF FAHD UNIVERSITY OF PETROLEUM & MINERALS 1 Mohammad Ali Jinnah University Department of Computer Science CS2420: Operations Research Semester Fall 2021 Dated: 13th October 2021 Due Date: 21st October 2021 (In class) Home Work # 1 NOTE: Please use graph paper attached for solving the problem(s). GRAPHICAL SOLUTION (30 points) 1. Consider the LP of the Reddy Mikks Formulation: Maximize ? = 3?1 + 2?2 Subject to ?1 + 2?2 ≤ 6 2?1 + ?2 ≤ 8 −?1 + ?2 ≤ 1 ?2 ≤ 2 ?1, ?2 ≥ 0 We already solved this in class. Add the following new constraint to the Reddy Mikks Problem, and change the objective to minimization. Solve it using Graphical Solution Method (using the objective function lines). (10 points) ?1 + ?2 ≥ 1 FORMULATION (20 points) 2. The Windsor Glass Company is planning to launch two new products. Product 1 is an 8-foot glass door with aluminum framing and Product 2 a 4x6 foot double-hung wood-framed window. • Aluminum frames are made in Plant 1, wood frames are made in Plant 2, and Plant 3 produces the glass and assembles the products. • Product 1 requires some of the production capacity in Plants 1 and 3, but none in Plant 2. • Product 2 needs only Plants 2 and 3. The marketing division has concluded that the company could sell as much of either product as could be processed by these plants. The management of the company wants to determine what mixture of both products would be the most profitable. The following table provides the information available. a) Formulate the problem as LP. b) and solve it using Graphical Solution (using the objective function lines). (10 points each) Plant Production time per batch, hours Production time available per week, hours Product 1 2 1 1 0 4 2 0 2 12 3 3 2 18 Profit per batch $3,000 $5,000 2