Resource Allocation The Enormous State University History Department offers three courses-Ancient. Medieval, and Modem History-and the department chairperson is trying to decide how many sections of each to offer this semester. The department may offer up to 45 sections total, up to 5,000 students would like to take a course, and there are 60 professors to teach them. (No student will take more than one history course, and no professor will teach more than one section.) Sections of Ancient History have 100 students each, sections of Medieval History have 50 students each, and sections of Modem History have 200 students each. Modern History sections are taught by a team of two professors, while Ancient History and Medieval History need only one professor per section. Ancient History nets the university $10,000 per section, Medieval nets $20,000 per section, and Modem History nets $30,000 per section. How many sections of each course should the department offer in order to generate the largest profit? What is the largest profit possible? Will there be any unused time lots, any students who did not get into classes, or any professors without anything to teach?
Trending nowThis is a popular solution!
Chapter 5 Solutions
FINITE MATHEMATICS >PRINT UPGRADE<
- Wholesale distribution Ace Electronics, Hi-Fi Stereo, and CD World buy a total of 175 DVD players from the same distributor each month. Because CD World buys 25 more units than the other two stores combined, CD Worlds cost is only 160 per unit. The players cost Hi-Fi 165 each and Ace 170 each. How many players does each retailer buy each month if the distributor receives 28,500 each month from the sale of the players to the three stores?arrow_forwardA commuter must travel from Ajax to Barrie and back every day. Four roads join the two cities. The commuter likes to vary the trip as much as posible, so she alwaysleaves and returns by different roads. In how many different ways can she make the round-trip?arrow_forwardSales Commissions A saleswoman works at a kiosk that offers three different models of cell phones: standard with 16 GB capacity, deluxe with 32 GB capacity, and super deluxe with 64 GB capacity. For each phone that she sells, she earns a commission based on the cell phone model. One week she sells 9 standard, 11 deluxe, and 8 super-deluxe and makes $740 in commission. The next week she sells 13 standard, 15 deluxe, and 16 super-deluxe for a $1204 commission. The third week she sells 8 standard, 7 deluxe, and 14 super-deluxe, earning $828 in commission. (a) Let x, y, and z represent the commission she earns on standard, deluxe, and super-deluxe, respectively. Translate the given information into a system of equations in x, y, and z. (b) Express the system of equations you found in part (a) as a matrix equation of the form AX=B . (c) Find the inverse of the coefficient matrix A and use it to solve the matrix equation in part (b). How much commission does the saleswoman earn on each model of cell phone?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning