IEEE 802.11ax is a promising standard for the next-generation WiFi network, which uses orthogonal frequency division multiple access (OFDMA) to segregate the wireless spectrum into time-frequency resource units (RUs). In this paper, we aim at designing an 802.11ax-based dense WiFi network to provide WiFi services to a large number of users within a given area with the following objectives: (1) to minimize the number of access points (APs); (2) to fulfil the users' throughput requirement; and (3) to be resistant to AP failures. We formulate the above into a joint AP placement and power-channel-RU assignment optimization problem, which is NP-hard. To tackle this problem, we first derive an analytical model to estimate each user's throughput under the mechanism of OFDMA and a widely used interference model. We then design a heuristic algorithm to find high-quality solutions with polynomial time complexity. Simulation results show that our algorithm can achieve the optimal performance for a small area of 50×50 m2. For a larger area of 100×80 m2 where we cannot find the optimal solution through an exhaustive search, our algorithm can reduce the number of APs by 32 ~ 55% as compared to the random and Greedy solutions.