Question

Answer the following question using Amdahl’s Law. Assume a computer system with three components, A, B, and C. Each component is used 40%, 35%, and 25% of the time, respectively. The components are used serially (i.e., not in parallel). The cost of this baseline system is $1,000. Assume that you are a manufacturer that has developed better implementations of these components, named A+, B+, and C+. The speedup of the better components compared to the original components is 1.25×, 1.3×, 1.2×, respectively. Assume that a customer is willing to pay more for a faster computer system proportional to the speedup (e.g., $1,100 for a system that is 1.1× as fast as the baseline system). What is the maximum price increase that you can charge for each of the better components, A+, B+, and C+?

- A) A+ = $125, B+ = $130, C+ = $120
- B) A+ = $150, B+ = $160, C+ = $140
- C) A+ = $112.5, B+ = $117, C+ = $108
- D) A+ = $120, B+ = $130, C+ = $110

Answer 1

According to Amdahl's Law, the maximum price increase for each of the better components, A+, B+, and C+, is $297.50.

Step-by-step explanation:

Amdahl's Law is a formula used to calculate the potential speedup of a computer system when only part of it is improved. In this case, we can use Amdahl's Law to determine the maximum price increase for each of the better components, A+, B+, and C+.

Step 1: Calculate the overall speedup of the system using the given percentages of component usage and speedup factors. The overall speedup is calculated as:

Overall speedup = (Speedup of A+ * Percentage usage of A) + (Speedup of B+ * Percentage usage of B) + (Speedup of C+ * Percentage usage of C)

Step 2: Calculate the maximum price increase for each component using the formula:

Maximum price increase = (Overall speedup - 1) * Baseline cost

Using the given speedup factors (1.25×, 1.3×, 1.2×) and component usage percentages (40%, 35%, 25%), we can calculate the overall speedup and maximum price increase for each component as follows:

A+ = (1.25 * 0.40) + (1.3 * 0.35) + (1.2 * 0.25) = 1.2975

Maximum price increase for A+ = (1.2975 - 1) * $1000 = $297.50

B+ = (1.25 * 0.40) + (1.3 * 0.35) + (1.2 * 0.25) = 1.2975

Maximum price increase for B+ = (1.2975 - 1) * $1000 = $297.50

C+ = (1.25 * 0.40) + (1.3 * 0.35) + (1.2 * 0.25) = 1.2975

Maximum price increase for C+ = (1.2975 - 1) * $1000 = $297.50