Assume that a company is selling a regular product with zero incremental cost. There are two types of customers in the market: there are 50 customers (Type A) whose willingness to pay is 60 dollars; there are 100 customers (Type B) whose willingness to pay is 100 dollars.

(a) What is the optimal price the company should set for this regular product? What is the optimal profit?

(b) should use excel solver) The company intends to implement a product versioning strategy. In order to achieve this, the company plans to damage some of the regular products to create an inferior version, which costs the company 1 dollar per unit. Type A customers' willingness to pay for the damaged product is 40 dollars. Type B customers' willingness to pay for the damaged product is 50 dollars. What are the optimal prices for the regular product and the damaged product respectively? Does this strategy increase the company's profit?