A student needs to enroll for a minimum of 60 credits. A student cannot enroll for
more than 70 credits. The credits are divided amongst project and three distinct
sets of courses namely, core courses, specialization courses, and elective courses.
It is compulsory for a student to enroll for exactly 15 credits of core courses and
exactly 20 credits of project. In addition, a student has to enroll for a minimum of
10 credits of specialization courses. The maximum credits of elective courses that
a student can enroll for is ______

Question

For positive real numbers 𝑆 and 𝐾, the function 𝐻𝐾(𝑆) is defined as:
𝐻𝐾(𝑆) = max(𝑆−𝐾, 0). The max function is defined as:
max(𝑎, 𝑏) = {𝑎,
when 𝑎> 𝑏
𝑏,
when 𝑎≤𝑏
The graph below shows the plot of a function 𝑁(𝑆) versus 𝑆.
𝑁(𝑆) can be expressed as _____.

Answer 1

Alternate approach - set up the credit equation directly: Let $E$ be elective credits and $S$ be specialization credits. Then:
$$15 + 20 + S + E = \text{Total}$$
Given constraints: $S \ge 10$ and $60 \le \text{Total} \le 70$. Rearranging gives $E = \text{Total} - 35 - S$.
Since $E$ increases as Total increases and decreases as $S$ increases, maximizing $E$ requires the largest Total (70) and the smallest $S$ (10).
So $E_{max} = 70 - 35 - 10 = 25$.
The maximum elective credits a student can enroll for is $25$.

Show Hint

The Correct Option is D

Solution and Explanation

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