(1) Determine the location that minimizes the sum of the Euclidean distance to the three points in the figure below, and that is outside of the infeasible region.
Assigned: Tue, 13 Sep (Groups of 2)
Due: 11:59p, Tue, 21 Sep
Group Members:
Please use the Code cells in this Jupyter notebook to answer each of the following questions. Please run all of the cells in your notebook and then submit it via Moodle. (There is a Run All Cells command under the Run menu.)
(1) Determine the location that minimizes the sum of the Euclidean distance to the three points in the figure below, and that is outside of the infeasible region.
(2) Continuing with Ex 2 from LP 3, just before purchasing the items, you found out that, in addition to the 50-pound weight limit, there is a maximum cube limit of five cubic feet. Since your clothes and the knapsack occupy two cubic feet, you will only be able to pack up to three cubic feet of purchased items. The table below from Ex 2 includes an additional column listing the density of each item in pounds per cubic foot.
│ Item Max_Order Sale_Price Purchase_Price Density
─────┼─────────────────────────────────────────────────────────
1 │ Coffee 40 6 2 32
2 │ Peppers 10 15 6 8
3 │ Ginger 2 8 1 30
4 │ Tea 5 25 5 2
5 │ Candy 15 4 2 20(2a) How many pounds of each item should be purchased?
(2b) Since addition cube capacity is available at an additional charge, what is the minimum increase in the cubic feet of items that can be packed that would maximize total profit?
(3) Continuing with Ex 4 from LP 2, it has been determined that the amount of corn in the feed cannot exceed forty-five percent of the total feed amount in order to not cause digestive difficulties for the animals. Determine the impact of this on the cost of the feed mix.
(4) Continuing with Ex 3 from LP 3, each product 1-3 has a production rate of 16, 8, and 3 L/hr, respectively.
(4a) Determine how many liters of each product should be produced if there are 12 hours in total available for production.
(4b) Continuing with 3a, determine if it would be a good idea to procure an additional 20 L of input 3 at \$5/L so that 50 L in total is available. Justify your answer.
Justification for 4b:
(4c) Continuing with 4a, determine if it would be a good idea to procure an additional 40 L of input 3 at \$5/L so that 70 L in total is available. Justify your answer.
Justification for 4c:
(5) The city utility board is considering constructing several mini generators to eliminate the need to purchase all their power. Each mini generator's capacity is 25 MW and the city's typical peak power requirements each month are 150, 160, 110, 175, 130, 150, 190, 200, 120, 100, 140, and 180 MW from January through December each year. Each mini generator needs to be off-line for three months each year for maintenance. The peak values are rough estimates, and power can be purchased (at a high price) to cover any shortfall in capacity. Determine the minimum number of generators the city needs to construct.