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An investment company would like to know which stocks to invest in to achieve maximum return....

An investment company would like to know which stocks to invest in to achieve maximum return. At the start of every day of the week (Monday through Friday) they decide how much to invest on that day, for example, X dollars. If in the next day they are able to match the initial investment (the X dollars) with another investment half that amount (X/2 dollars) they can expect a total return on the third day that doubles the initial amount of the investment (a total return of 2X dollars). For example, if the trader invests X dollars on Monday and X/2 dollars on Tuesday, which in total is 1.5X dollars, they can expect to receive 2X dollars on Wednesday, which gives them a gain of 0.5X dollars in two days.

However, any investment that is not matched on the subsequent day will lose its entire value.

There is also the Foreign Exchange (FX) market. The firm noticed that whenever there are a lot of travelers during the weekend, the FX rate tends to increase in the following few days and go back to normal by the end of the week. They believe that if they invest Y dollars in the FX market on the Monday right after the weekend, they can receive its doubled amount (2Y) on Tuesday, if the investment is made on Wednesday, the only receive 1.2Y dollars in two days (Friday). No investment in FX markets will be considered for the days after Wednesday.

On any day of the week, the firm can re-invest any return they receive from previous investments made in the same week. If there is any amount in the firm's account that amount can accrue 1% of daily interest through money markets.

Every Sunday the firm must decide how much money in their account should be invested each day. They want to maximize the amount of money they have in their account by the end of the coming Saturday. The firm currently has 1 million in their account.

Question: Solve this problem by using a Linear Programming (LP) model. Show the objective function, decision variables, and the constraints. (No need to find the optimal solution)

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