A car manufacturing company is bankrupted and is going to close the factory very soon. This company has some spare items, which either can be sold directly to other manufacturers, or assembled to make more valuable intermediate products. In the later case, the company can sell the assembled products with much better prices to other manufacturers. The information about the number of available spare items and their prices (when sold directly) are provided in the 3rd and 4th column of Table 1.

Table 1. Information about spare items

The sales price of assembled products in the market and the number of spare items that each one requires for assembly are provided in Table 2.

The company is looking for the best plan to get rid of the available spare items before its closure.

Question 1: Formulate this problem as a mathematical programming model. Define components of the model including indices, sets, parameters, decision variables, the objective function, and constraints precisely (In order to avoid confusion, I recommend that you introduce a set for spare items and a set for assembled products. Also instead of working with given numbers in the tables, I recommend that you introduce appropriate parameters)