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linear programming problem graphically




1. Solve the following linear programming problem graphically;maximize 2X1 3X2;subject to X1 8;X2 6;X1 2X2 16;X1, X2 0;Units of K per period;B4;(8, 16);C4;(6.5, 20);A4;(16, 16);I4;I3;I I 2 1;Feasible region;Units of L per period;D4;(4, 32);F I G U R E 4;Solution to a Cost;Minimization Problem;TA B L E 5;Total Cost at Extreme Points;Value of variable;Extreme point K L Total cost;(4,32) 4 32 $160;(6.5,20) 6.5 20 132;(8,16) 8 16 128;(16,16) 16 16;2. In problem 1, how would the optimal solution change if the restrictions imposed (i.e.;the ri?s) were all cut in half?;3. Solve the following linear programming problem using the general solution method;minimize C 3X1 4X2;subject to X1 X2 2;2X1 4X2 5;X1, X2 0;4. Form the dual to the linear programming problem presented in problem 3, then solve;it to obtain the optimal value of C. Does the minimum value of C for the primal in;Problem 3 equal the maximum value of C;in the dual for this problem?;5. The advertising manager at Cadillac wishes to run both television and magazine ads to;promote the new Cadillac GTS in the greater Chicago area market. Each 30-second television;ad will reach 30,000 viewers in the target age group of buyers 35 to 55 years old.;Running one full page ad in Cool Driver magazine will reach 10,000 readers in the 35;to 55 year-old target market. To further promote the new GTS, the manager wishes to;stimulate prospective buyers to come in to Chicago area dealerships to test drive the;GTS. Past experience in Chicago indicates that a television ad will generate 500 test drives;while a magazine ad will generate only 250 test drives.;In order to reach the desired level of new-model penetration in the Chicago area, the;advertising manager believes it is necessary to reach at least 90,000 potential buyers in;the 35 to 55 age bracket and to get at least 2,000 of these potential buyers to take a test;drive. Each 30- second TV ad costs $100,000 and each magazine ad costs $40,000. In;reaching these objectives, the manager wishes to minimize the total expenditure on TV;and magazine ads.;a. State the linear programming problem facing this advertising manager. Be sure to;formulate the objective function and inequality constraints (including appropriate;non-negativity constraints).;b. Solve the linear programming problem. What is the optimal number of TV ads and;magazine ads? What will be the minimum possible level of total expenditures on;television and magazine ads necessary to successfully promote the GTS in Chicago?;c. Suppose the local television stations, in order to reduce set-up costs, require Cadillac;to run its ad two or more times. How would this constraint alter the solution to this;linear programming problem?


Paper#25715 | Written in 18-Jul-2015

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