91Ó°ÊÓ

The Enormous State University History Department offers three courses, Ancient, Medieval, and Modern History, and the chairperson is trying to decide how many sections of each to offer this semester. The department is allowed to offer 45 sections total, there are 5,000 students who would like to take a course, and there are 60 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History hold 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of 2 professors, while Ancient and Medieval History need only 1 professor per section. How many sections of each course should the chair schedule in order to offer all the sections that they are allowed to, accommodate all of the students, and give one teaching assignment to each professor? HIIT [See Example 2.]

Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. \(3.1 x-4.5 y=6\) \(4.5 x+1.1 y=0\)

The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, \(A Z\) and Toronto, Ontario. You have been given the job of coordinating distribution of the latest model, the Gladiator, to outlets in Honolulu and Venice Beach. The Tucson plant, when operating at full capacity, can manufacture 620 Gladiator boards per week. while the Toronto plant, beset by labor disputes, can produce only 410 boards per week. The outlet in Honolulu orders 500 Gladiator boards per week, while Venice Beach orders 530 boards per week. Transportation costs are as follows: Tucson to Honolulu: \(\$ 10\) per board; Tucson to Venice Beach: \(\$ 5\) per board. Toronto to Honolulu: \(\$ 20\) per board; Toronto to Venice Beach: \(\$ 10\) per board. a. Assuming that you wish to fill all orders and assure full capacity production 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? b. Is there a way of doing this for less money? HINT [See Example 4.]

You have a mixture of Designer Whey and Muscle Milk that costs a total of \(\$ 14\) and supplies exactly \(104 \mathrm{~g}\) of carbohydrates. How many grams of protein does it supply?

Supply and Demand (from the GRE Economics Test) In the market for soybeans, the demand and supply functions are \(Q_{D}=100-10 P\) and \(Q_{S}=20+5 P\), where \(Q_{D}\) is quantity demanded, \(Q_{S}\) is quantity supplied, and \(P\) is price in dollars. If the government sets a price floor of \(\$ 7\), what will be the resulting surplus or shortage?

What is meant by a pivot? What does pivoting do?

You are row-reducing a matrix and have chosen a \(-4\) as a pivot in Row 2 . Directly below the pivot, in Row 4 , is a \(-6\). What row operation can you use to clear the \(-6 ?\)