Situation The City Council proposed to utilize a government-owned land with an area of 12,150 square meters. One-third of it will be used for a picnic area while the rest of the land will be planted by mango trees. As the city engineer, you were tasked to determine the following: 1. the dimensions of the picnic area with minimum cost of fencing given that area is to be rectangular and to be fenced off on three sides not adjacent to the highway. 2. the number of mango trees that leads to a maximum yield given that if 50 trees are planted, the average yield per tree will be 400 kilos while the average yield will decrease by 2 kilos per tree for each additional tree on the same area due to overcrowding.
Situation The City Council proposed to utilize a government-owned land with an area of 12,150 square meters. One-third of it will be used for a picnic area while the rest of the land will be planted by mango trees. As the city engineer, you were tasked to determine the following:
1. the dimensions of the picnic area with minimum cost of fencing given that area is to be rectangular and to be fenced off on three sides not adjacent to the highway.
2. the number of mango trees that leads to a maximum yield given that if 50 trees are planted, the average yield per tree will be 400 kilos while the average yield will decrease by 2 kilos per tree for each additional tree on the same area due to overcrowding.
Verify that the value/s is/are extremum/extrema using either first/second derivative test.
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