problem1)
Solve the following linear programming problem graphically:
maximize 2X1 + 3X2
subject to X1 <= 8
X2 <= 6
X1+ 2X2 <= 16
X1, X2 >=0
problem2)
In problem 1, how would optimal solution change if restrictions imposed (i.e., the r_{i}’s) were all cut in half?
problem3)
Solve following linear programming problem using general solution method:
minimize C = 3X1 + 4X2
subject to X1 + X2 >= 2
2X1 +4X2 >=5
X1, X2 >= 0
problem4)
Form dual to the linear programming problem presented in problem 3; then solve it to get optimal value of C° . Does minimum value of C° for the primal in Problem 3 equal the maximum value of C° in dual for this problem?
problem5)
Advertising manager at Cadillac wishes to run both television and magazine ads to promote new Cadillac GTS in the greater Chicago area market. Each 30-second television ad will reach 30,000 viewers in 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, manager wishes to stimulate prospective buyers to come in to Chicago area dealerships to test drive the GTS. Past experience in Chicago indicates that the television ad will generate 500 test drives, whereas the magazine ad will generate only 250 test drives. In order to reach desired level of new-model penetration in the Chicago area, advertising manager believes it is essential 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 the 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 linear programming problem facing this advertising manager. Be sure to formulate objective function and inequality constraints (including appropriate non-negativity constraints).
b) Solve 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?