Assigned: Thu, 2 Sep (Groups of 2)
Due: 11:59p, Thu, 9 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) Two different medical technologies are being considered. The first requires more labor input but would require only \$20 million per year to finance the equipment used; the annual cost to produce $x$ grams of output has been estimated to be $20 + 12x^{2/3}$. The second technology is more automated but requires \\$50 million per year to finance; its annual cost has been estimated to be $50 + 8x^{1/2}$. Determine the grams per year at which both technologies would have the same cost.
(2) Forty potential sites for tracking devices have been identified throughout a wildlife preserve. Dedicated fiber-optic cables will be installed in a straight line from each tracking device to a station that can receive input from up to five devices.
(2a) Determine the location for the station, and at which sites tracking devices should be installed so that the total length of cable is minimized. The coordinates of the potential sites can be generated by running the following code:
using Random
Random.seed!(93645)
P = 1000*rand(40,2)
(2b) Describe (in words, no code) a possible procedure to install tracking devices at each site if seven additional identical receiving stations were to become available.
Your Procedure:
(3) Use the 7-weeks of data in the file _NLOpt-3-Data.csv to answer the following questions:
(3a) Determine the total profit for all of the procedures listed in the last table of Ex 2 in _2-NLOpt-3 notebook except for multiple regression (this is because there are no website visitor data in the file).
(3b) Determine what day 50's size should be if 350 orders have been received at the beginning of day. Justify your answer.
Justification:
(3c) The \$1 cost to bake each loaf of bread used in the analysis only includes the cost of ingredients and the direct labor cost of the baker. It has been estimated that it cost an additional \\$500 to fuel the oven each day for baking the bread, irrespective of the number of loaves baked in the oven. Since order data is available each morning, determine the impact on total profits if no bread were baked any day that the orders were below a threshold of 100, thereby saving \$500 for that day.
(3d) Describe (in words, no code) a possible procedure to determine the optimal threshold to use.
Your Procedure: