quant solutions

# Quant solutions - West Team(Hodgetts Problem 2-36 from the book As part of a quality improvement initiative Consolidated Electronics employees

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West Team (Hodgetts) Problem 2-36 from the book As part of a quality improvement initiative, Consolidated Electronics employees complete a three-day training program on teaming and a two-day training program on problem solving. The manager of quality improvement has requested that at least 8 training programs on teaming and at least 10 training programs on programs on problem solving be offered during the next six months. In addition, senior-level management has specified that at least 25 training programs must be offered during this period. Consolidated Electronics uses a consultant to teach the training programs. During the next quarter, the consultant has 84 days of training time available. Each training program on teaming costs \$10,000 and each training program on problem solving costs \$8000. A) Formulate a linear programming model that can be used to determine the number of training programs on teaming and the number of training programs on problem solving that should be offered in order to minimize total cost. B) Graph the feasible region C) Determine the coordinates of each extreme point D) Solve for the minimum cost solution Solution: Part A Decision variables: T- # of teaming training programs PS- # of Problem Solving programs Objective is to Minimize costs Min T (10000) + PS (8000) Constraints Consultant can work 84 hours per quarter or 168 for 6 months At least 25 training programs offered A minimum of 8 teaming programs offered over a 6 month period A minimum of 10 Problem Solving programs offered over a 6 months period Constraint Formulas T>=8 PB.>=10 T+PB>=25 3T + 2PB<=168

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Part B , C and D– Graph the solution Extreme point are T=8 (Teaming) and PS (Problem Solving) = 17 and minimum cost is \$216,000
Problem from the book (3-21) 3-21 Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Savor, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Rental Class Super Savor Deluxe Business Room Type I \$30 \$35 ---- Typle II \$20 \$30 \$40 Type I rooms do not have Internet access and are not available for the Business rental class. Round Tree’s Management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. A) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Is the demand by any rental class not satisfied? Explain B) How many reservations can be accommodated in each rental class? C)

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## This note was uploaded on 03/15/2011 for the course ECON 101 taught by Professor Dezhbakhsh during the Spring '07 term at Emory.

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Quant solutions - West Team(Hodgetts Problem 2-36 from the book As part of a quality improvement initiative Consolidated Electronics employees

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