full solution and explanation

4. Sida has a total of 100 hours per week that can be allocated to two types of activities: harvesting mangosteen in the garden for eating or selling and fishing. The number of mangosteen harvested per week is 2V LM kg. LM indicates the number of hours used to store mangosteen. The quantity of fish caught per week is V LF , where LF indicates the number of hours it takes to catch fish. The utility that Sida gained from consuming mangosteen and fish is shown by M' F ,where M and F represent the quantity of mangosteen and fish consumed by Sita. Neighbors are willing to send Sida to sell and buy things at a fresh market in a seaside town. Sida found that at this market, the price of one kilogram of mangosteen was three times of a kilogram of fish. In this case, How should Sida plan the production and consumption of mangosteen and fish to achieve the maximum utility? (10 points)