You have built a REST API using API gateway and distributed to your customers. However, your API is receiving large number of requests and overloading your backend system causing performance bottlenecks and eventually causing delays and failures in serving the requests for your important customers. How would you improve the API performance? (Choose 2 options)

Answer options:

A.Enable throttling and control the number of requests per second.
B.Create a resource policy to allow access for specific customers during specific time period.
C.Enable API caching to serve frequently requested data from API cache.
D.Enable load balancer on your backend systems.

Answer: A, C
Option A is correct. To prevent your API from being overwhelmed by too many requests, Amazon API Gateway throttles requests to your API. Specifically, API Gateway sets a limit on a steady-state rate and a burst of request submissions against all APIs in your account.
For more information on throttling, refer documentation here. 
https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-request-throttling.html
Option B is not correct. This is not a viable solution. Resource policies cannot have a time range based condition.
Following documentation shows the conditions supported for API Gateway resource policies.
https://docs.aws.amazon.com/apigateway/latest/developerguide/apigateway-resource-policies-aws-condition-keys.html
Option C is correct. You can enable API caching in Amazon API Gateway to cache your endpoint’s responses. With caching, you can reduce the number of calls made to your endpoint and also improve the latency of requests to your API. When you enable caching for a stage, API Gateway caches responses from your endpoint for a specified time-to-live (TTL) period, in seconds. API Gateway then responds to the request by looking up the endpoint response from the cache instead of making a request to your endpoint. The default TTL value for API caching is 300 seconds. The maximum TTL value is 3600 seconds. TTL=0 means caching is disabled.
For details on enabling caching, refer documentation here. 
https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-caching.html#enable-api-gateway-caching
Option D is not correct. We can improve performance by increasing the capacity of backend systems if above settings does not help. Simply adding a load balancer does not improve any performance.