Case Study Challenge
Solar Panel Design Optimization
A technical company is designing a rectangular solar panel installation on a roof using 300 metres of boundary material.
The design includes a partition running parallel to one of the sides, dividing the area (roof) into two sections.
Let the length of the side perpendicular to the partition be x metres and the side parallel to the partition be y metres.
Answer the following:
| (i) | Write the equation for the total boundary material used in terms of x and y. | [1 Mark] |
| (ii) | Write the area of the solar panel as a function of x. | [1 Mark] |
| (iii) | (a) Find the critical points and use the Second Derivative Test to determine maximum area.
— OR —
(b) Use the First Derivative Test to calculate the maximum enclosable area. |
[2 Marks] |