(A) Find the Total Number of Additions and Multiplications That $\text { for } i:=1 \text { to } n$

question 14

Essay

(a) Find the total number of additions and multiplications that must be performed when the following algorithm is executed. Show your work carefully.
$\text { for } i:=1 \text { to } n$
$\text { for } j=i \text { to } n$
$a:=2 \cdot(5 \cdot i+j+1)$
$\text { next } j$
$\text { next } i$
(b) Find an order for the algorithm segment of part (a) from among the following: $\log _ { 2 } n , n$ , $n \cdot \log _ { 2 } n , n ^ { 2 } , n ^ { 3 }$ , and $n ^ { 4 }$ . Give a reason for your answer.

---

Definitions:

Differential Analysis

A decision-making technique that involves comparing the costs and benefits of alternative actions.

Accumulated Depreciation

The total amount of depreciation expense that has been recorded against a fixed asset up to a specific date, reflecting its wear and use over time.

Salvage Value

The estimated residual value of an asset at the end of its useful life, often considered in depreciation calculations.

Normal Plant Capacity

The expected or planned level of operation for a manufacturing plant, considering normal working conditions and time periods.