A pipeline for transporting oil will connect two points A and B that are 3 miles apart on opposite banks of a straight river that is 1 mile wide. Part of the pipeline will run under the water from point A to a point C on the opposite bank, and then above ground from point C to point B.
If the costs per mile for running the pipeline under the water is 4 times the cost per mile of running it above ground, find the location of point C that will. minimize the total cost.

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)