Applications: System of equationsName:

Math 156

Name:

Solve using Matrices

  1. Your hamburger stand at the fair is closing in about a half an hour and you have 15 opened slices of cheese, 13 bread rolls and 19 defrosted beef patties. Rather than throw it all out, you decide to cook up the rest and sell them at a discount. Plain burgers each require one beef patty and one bread roll, regular cheeseburgers require one beef patty one slice of cheese and one bread roll. A double cheeseburger uses two beef patties two slices of cheese and one bread roll. How many of each type of burger should you make?
  1. Enormous University History Department offers three courses for undergraduates; Ancient, Medieval, and Modern History. The chair of the department is trying to decide how many sections of each to offer this quarter. The department is allowed to offer 45 sections total. There are 5000 students who would like to take a history course, and there are 60 professors to teach them. Sections of Ancient History hold 100 students each, sections of Medieval History hold 50 students each, and sections of Modern History hold 200 students each. Modern History sections are taught by a team of two professors, whereas Ancient and Medieval History need only one professor per section. How many sections of each course should the chair schedule in order to offer all the sections allowed, accommodate all the students, and give teaching assignments to all of the professors?
  1. The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, AZ and TorontoOntario. You have been given the job of coordinating distribution of the latest model, the Gladiator, to their outlets in Honolulu and VeniceBeach. The Tucson plant, when operating at full capacity, can manufacture 620 Gladiator boards per week, whereas the Toronto plant, beset by labor disputes, can produce only 410 boards per week. The outlet in Honolulu orders 500 boards per week and VeniceBeach orders 530 boards per week. Transportation costs for a single board are summarized in the table below. Assuming that you wish to fill all the orders and assure full capacity at both plants, is it possible to meet a total transportation budget of $10,200? If so, how many Gladiator boards are shipped from each manufacturing plant to each distribution outlet?

Transportation Costs / FROM
Tucson / Toronto
TO: / VeniceBeach / $5 / $10
Honolulu / $10 / $20

4. Three one way streets intersect as shown in the diagram below. Traffic counters are set up on each of the approaching streets, and their results are given in the boxes.. Find the number of cars that travel down each side of the triangle.