To buy a new house you must borrow . To do this you take out a ​, ​-year, percent mortgage. Your mortgage​ payments, which are made at the end of each year​ (one payment each​ year), include both principal and percent interest on the declining balance. How large will your annual payments​ be?

Suppose an economy consists of three sectors: energy (e), manufacturing (m), and agriculture (a). sector e sells 70% of its output to m and 30% to a. sector m sells 30% of its output to e, 50% to a, and retains the rest. sector a sells 15% of its output to e, 30% to m, and retains the rest.

Needs to schedule the staffing of the center. it is open from 8am until midnight. larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required: time of dayminimum number of consultants required to be on duty8 am-noon4noon-4 pm84pm-8pm108pm-midnight6 two types of computer consultants can be hired: full-time and part-time. the full- time consultants work for eight consecutive hours in any of the shifts: morning (8am- 4pm), afternoon (noon-8pm) and evening (4pm-midnight). full-time consultants are paid $14 per hour. part-time consultants can be hired to work any of the four shifts listed in the table. part-time consultants are paid $12 per hour. an additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty. larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost. formulate this as an lp problem. you must define your variables clearly

Sarah salesrep is brand new to her job selling "lifetime" printers that never need replacement ink cartridges. the problem is that these printers cost ten times more than a regular printer, so it is difficult to get prospective buyers to understand the cost savings of buying it. to break through the barrier and begin making sales, sarah should use a analysis that highlights her printer's lower cost.