Part II. Formulate a linear programming model. Note: You don\'t need to find the
ID: 368886 • Letter: P
Question
Part II. Formulate a linear programming model. Note: You don't need to find the optimal solution The management at an energy drink company wants to decide how many TV ads and magazine ads to run during the next quarter. Each TV ad costs $5,000 and is expected to increase the sales by 300,000 cans. Each magazine ad costs $2,000 and is expected to increase the sales by 500,000 cans. A total of $100,000 may be spent on TV and magazine ads; however, the management wants to spend no more than $70,000 on TV ads and no more than $50,000 on magazine ads. Furthermore, the management specifies that the total number of ads should be at least 30 and the number of' TV ads should be at least 12. Please formulate a linear programming model for this problem. Follow the steps below. 1. Define the decision variables 2. Write the obiective in terms of the decision variables. 3. Write all the constraints in terms of the decision variables.Explanation / Answer
(1)
T = Number of TV ads
M = Number of Magazine ads
(2)
Objective Function: max.Z = Total sales increase = 300,000T + 500,000M
(3)
Subject to,
5,000T + 2,000M 100,000 (Maximum total budget)
5,000T 70,000 (Maximum TV ad expense)
2,000M 50,000 (Maximum Magazine expense)
T + M 30 (Minimum total no. of ads)
T 12 (Minimum TV ads)
T, M 0 (Non-negativity)