Design efficient algorithms that take an array of positive numbers a, and determine:
a. the maximum value of a[j] + a[i], with j ≥ i.
b. the maximum value of a[j] - a[i], with j ≥ i.
c. the maximum value of a[j] * a[i], with j ≥ i.
d. the maximum value of a[j] / a[i], with j ≥ i.