Question Video: Optimization Using Inequalities Mathematics

Video Transcript

Given that 𝑥 is greater than or equal to negative five and less than or equal to 10 and 𝑦 is greater than or equal to negative seven and less than or equal to four, find the greatest possible value of 𝑥 plus 𝑦.

As we need to find the greatest possible value of two variables 𝑥 and 𝑦, we need both values to be as large as possible. The maximum possible value of 𝑥 is 10 as 𝑥 must be less than or equal to 10. In the same way, we see that the maximum possible value of 𝑦 is four as 𝑦 is less than or equal to four. The greatest possible value of 𝑥 plus 𝑦 is therefore equal to 10 plus four. This is equal to 14. If 𝑥 is greater than or equal to negative five and less than or equal to 10 and 𝑦 is greater than or equal to negative seven and less than or equal to four, then the greatest possible value of 𝑥 plus 𝑦 is 14.