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.

The City Council proposed to utilize a government-owned land with an area of 9,600 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: 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 70 trees are planted, the average yield per tree will be 300 kilos while the average yield will decrease by 3 kilos per tree for each additional tree on the same area due to overcrowding.   As an Engineer, cite other instances aside from the situations given above where optimization (one minimization) can be applied.

The City Council proposed to utilize a government-owned land with an area of 15, 000 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the following: 1. The dimensions of the land planted with mango trees 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 rate at which the total average of COVID cases is increasing at x = 10 tents and dx/dt = 1 tent per day, given than if 25 tents are built, the average number of COVID cases per tent will be 6 cases while the average number of cases will increase by 2 per tent for each additional tent in the same area due to overcrowding. Verify that values are extrema using either the first derivative test or second derivative test. As an engineer, cite other instances aside from the situations given above where…

The City Council proposed to utilize government-owned land with an area of 9,600 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the following: 1. the dimensions of the land planted with mango trees 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. A. Illustration and Representation of Variables B. Detailed Solution C. Conclusion D. As an Engineer, cite other instances aside from the situations given above where optimization (one maximization and one minimization) can be applied. 2. the rate at which the total average number of COVID cases is increasing at x = 10 tents and dx = 1 tent per day, given that if 20 tents are built, the average number of COVID cases per tent will be 5 dt cases while the average number of cases will increase by 2 per tent for…