Suppose you have constructed a multi-layer perceptron (MLP) as below to predict the unit housing price (dollars per square feet) of an apartment, based on predictors like 1 (number of bedrooms), 2 (floor number). The activation functions used for all layers in the MLP are assumed to be ReLU (rectified linear unit). It is assumed that the currently available house types for sales include 3-bedroom, 4-bedroom, and 5-bedroom, across each floor from level 6 to 8 in the block. The total budget you have for housing is $450,000 and you are planning to buy an apartment with at least 630 square feet.

Compute manually the predicted unit housing price for a 4-bedroom apartment on the 6th floor. (Remark: Write down the intermediate steps for the computation). (5 marks)

(b) (Python Code) The above manual computation can be tedious. As such, formulate a Python program to automate the computation. Predict the unit housing price in part (a) again and save a screenshot of the model output from running your code. (10 marks)

(c) Among all the available house types, which house types (example format to present your answer: 4-bedroom on floor 8) can you afford to buy? Explain your reasons. (Word limit: 100 words) (5 marks)

(d) Evaluate what is the marginal cost in unit housing price (dollars per square feet) for an upgrade of one additional bedroom? What is the marginal cost for an upgrade of one floor higher? (Word limit: 100 words) (5 marks)

(e) If the activation function is changed from ReLU to sigmoid, can you still compute the marginal cost the same way as in part (d) and why? (Word limit: 100 words) (5 marks)

(f) It is assumed that an upgrade of an apartment to a higher floor or a larger number of bedrooms will give you higher living utility (e.g. comfort of living). As a resident, you always prefer the apartment with higher living utility. In addition, the marginal living utility obtained from one additional floor and one additional bedroom are assumed to be the same. Among all the affordable house types you identified in part (c), which house type will you choose and explain why. (Word limit: 100 words)