Quantitative Analysis

Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type, and there should be no more than 19 ads in total. The company does not want the number of newspaper ads to exceed the number of radio ads by more than 25 percent. Each newspaper ad reaches 6,000 people, 50 percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of whom will respond.

The company wishes to reach as many respondents as possible while meeting all the constraints stated. 1. Develop the appropriate LP model for determining the number of ads of each type that should be placed. 2. Graph the constraints and identify the feasible region (clearly indicate the feasible region) 3. Solve the LP problem using e corner point method and comment on your findings. CASE PROBLEM 1 1) RadioNewspaperMin/Max Cost4006007200 Max Min1115 Min Max1119 Max At least 2R11 Min At least 2N12 Min N ? 1. 25R Objective: 20 (2000)5 (6000) R = # Radio ads N = # Newspaper ads Therefore A= . 20(2000) R + . (6000) N Constraints 400 R + 600N ? 7200 R + N ? 15 R + N ? 19 R ? 2 N ? 2 R, N ? 0 1. 25 R – N ? 0 2) 400R+ 600N ? 7200 (4R + 6N ? 72) R= (0, 18)N= (12, 0) R + N ? 15 R= (0, 15)N= (15, 0) R + N ? 19 R= (0, 19)N= (19, 0) R ? 2 Vertical line N ? 2 Horizontal line 1. 25 R – N ? 0 R= (0, 10)N= (0, 12. 5) [pic] 3) Corner Point 1: R+N = 15 4R+6N = 72 Therefore C (9,6) = 21,600 Corner Point 2: N = 2 4R+6N = 72 Therefore C (15,2) = 12,000 Corner Point 3: R = 2 R+N =15 Therefore C (13,2) = 11,200 Conclusion: The corner point 1 with the value of 21,600; is the value at which the objective function is at a maximum.

The co-ordinates of this vertex is the optimal solution and the value of is the optimal value |Corn flakes | | |XOGCC |Weight of oats in Corn flakes | |XCGCC |Weight of corn in Corn flakes | |XSCGCC |Weight of Sugar in Corn flakes | |XMNGCC |Weight of mixed nuts in Corn flakes | |XSCGCC |Weight of shredded coconut in Corn flakes | |XMSGCC |Weight of milk solids in Corn flakes | |XDFGCC |Weight of dried fruits in Corn flakes | | | |Warehouses | |Factory | Warehouse |R1 |R2 |R3 |R4 |R5 |R6 |R7 | |W1 |11 (a1) |22 (a2) |51 (a3) |41 (a4) |11 (a5) |22 (a6) |31 (a7) | |W2 |12 (b1) |24 (b2) |42 (b3) |32 (b4) |22 (b5) |11 (b6) |22 (b7) | |W3 |29 (c1) |21 (c2) |39 (c3) |40 (c4) |22 (c5) |29 (c6) |39 (c7) | |Demand |301 |322 |339 |310 |422 |434 |200 | |

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