Questions: Assume that XYZ company is selecting TV, Radio, Newspaper, and Magazine ads to increase the volume of their customers. The company has 26,000 for advertisement purposes. The cost per advertisement for TV, Radio, Newspaper, and Magazine are 150, 100, 80, and 40, respectively. They do not want to spend more than 15,000 on Newspaper and Magazine ads. The number of Newspaper ads should be at least twice the Magazine ads. The total number of ads all together should not be less than 330 and not more than 360, and the maximum amount spent on TV ads should be less 1,600. They should have a minimum of 10 TV ads. Which resource do they run out first after running the problem through Excel's Solver?

Question 11: Which resource do they run out first after running the problem through Excel's Solver?

Step 1: Define the decision variables

Let:

• \( x_1 \) = number of TV ads
• \( x_2 \) = number of Radio ads
• \( x_3 \) = number of Newspaper ads
• \( x_4 \) = number of Magazine ads

Step 2: Formulate the constraints

1. Budget constraint:
   \( 150x_1 + 100x_2 + 80x_3 + 40x_4 \leq 26,000 \)
2. Newspaper and Magazine budget constraint:
   \( 80x_3 + 40x_4 \leq 15,000 \)
3. Newspaper ads should be at least twice Magazine ads:
   \( x_3 \geq 2x_4 \)
4. Total number of ads constraint:
   \( 330 \leq x_1 + x_2 + x_3 + x_4 \leq 360 \)
5. Maximum amount spent on TV ads:
   \( 150x_1 \leq 1,600 \)
6. Minimum number of TV ads:
   \( x_1 \geq 10 \)

Step 3: Analyze the constraints

• The maximum amount spent on TV ads is \( \$1,600 \), which limits \( x_1 \) to \( x_1 \leq \frac{1,600}{150} \approx 10.67 \). Since \( x_1 \) must be an integer, \( x_1 \leq 10 \).
• Combining this with the minimum \( x_1 \geq 10 \), we get \( x_1 = 10 \).
• Substituting \( x_1 = 10 \) into the budget constraint:
  \( 150(10) + 100x_2 + 80x_3 + 40x_4 \leq 26,000 \)
  Simplifies to:
  \( 100x_2 + 80x_3 + 40x_4 \leq 24,500 \)

Step 4: Determine the binding constraint

• The binding constraint is the one that limits the solution the most. Here, the budget constraint \( 100x_2 + 80x_3 + 40x_4 \leq 24,500 \) is likely to be the first resource to run out, as it directly limits the number of ads for Radio, Newspaper, and Magazine.

Step 5: Conclusion

The resource that runs out first is the budget for Radio, Newspaper, and Magazine ads.

\\(\boxed{\text{The budget for Radio, Newspaper, and Magazine ads runs out first.}}\\)