In a given year, the population of Metro City is 7420, and the population is decreasing by 152 people per year. The population of Smallville is consistently 1200 less than half of Metro City. Determine how long it will take for Smallville's population to reach 2282. Which answer provides the correct equation and solution for the situation, where x represents the number of years?

A. The equation is 2282=2(7420−152x)+1200. It will take 45.26 years for the population of Smallville to be 2282 people.
B. The equation is 2282=2(7420−152x)+1200. It will take 45.26 months for the population of Smallville to be 2282 people.
C. The equation is 2282=12(7420−152x)−1200. It will take 3 months for the population of Smallville to be 2282 people.
D. The equation is 2282=12(7420−152x)−1200. It will take 3 years for the population of Smallville to be 2282 people.

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.)