1. GMW Auto manufactures luxury cars and trucks. The company believes that its m

Question

1. GMW Auto manufactures luxury cars and trucks. The company believes that its mostlikely customers are high-income women and men. To reach these groups, GMW Auto has embarked on an ambitious TV advertising campaign and has decided to purchase commercial spots on two types of programs: Drama show and Super Bowl game. A drama show commercial's length is 1.4-minutes and each drama show commercial is seen by 12 million high-income women and 8 million high-income men. A Super Bowl commercial's length is 0.5-minute and each Super Bowl commercial is seen by 11 million high-income women and 16 million high-income men. GMW Auto has 4.7-minutes of commercial spots available. A 1.4-minutes drama show ad costs $246,000, and a 0.5-minute Super Bowl ad costs $457,000. GMW would like the commercials to be seen by at least 47 million high-income women and 35 million high-income men.

a) Formulate a linear programming model to determine how GMW Auto can meet its advertising requirements at minimum cost. (Write the complete model for the problem. Make sure to give clear de nitions of your decision variables).

b) Solve the problem by using Excel Solver (Hand-in the value and formulas printouts for the problem). Show the optimal solution and optimal value in your printouts.

Please show all work and detailed constraints! Thank you!

Explanation / Answer

let x be number of Drama show commercials and y be the number of Super Bowl commercials

Minimize cost = 246000x + 457000y
subject to,
1.4x + 0.5y <= 4.7 -- Time constraint
12x + 11y >= 47 -- minimum high income women constraint
8x + 16y >= 35 -- minimum high income men constraint

Solving this problem using excel solver gives optimal solution

Below is the output of excel solver

Hence as per the optimal solution, there should be 3 Drama show ads and 1 Super bowl add. This will result into minimum cost of $1195000.

Solver Solution x y Total Demand Decision Variables 3 1 Cost 246000 457000 1195000 Constraint 1 1.4 0.5 4.7 4.7 Constraint 2 12 11 47 47 Constraint 3 8 16 40 35

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