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Lial M.L. Mathematics with Applications in the Management, Natural, and Social Sciences, Tenth Edition
62. Two people with flu visited a college campus. The number of days, T, that it took for the flu virus to infect n people is given by the equation
T= -1.43 ln ((10,000 - n) / 4998n)
How many days will it take for the virus to infect
(a) 500 people?
(b) 5000 people?
1. The U-drive Company in Example 1 learns that each van now costs $13000 and each small track $18000. The company decides to buy only 182 new vehicles. How many of each kind should it buy?
2. Suppose that Ellen McGillicuddy in Example 2 finds that her annual return on the international stock fund will be only 4%. Now how much should she put in each investment?
3. To meet consumer demand, the animal feed in Example 3 now supplies only 2400 units of fat. How many units of corn, soybeans, and cottonseed are now needed?
4. Suppose that Kelly Karpet Kleaners in Example 5 finds a way to pack the EZ model in an 8-cubic-foot box. Now how many of each model should a fully loaded van carry?
5. Matt took clothes to the cleaners three times last month. First, he brought 3 shirts and 1 pair of slacks and paid $10.96. Then he brought 7 shirts, 2 pairs of slacks, and a sports coat and paid $30.40. Finally, he brought 4 shirts and 1 spots coat and paid $14.45. How much was he charged for each shirt, each pair of slacks, and each sports coat?
6. Business A minor league baseball park has 7000 seats. Box seats cost$6, grandstand seats cost $4, and bleacher seats cost $2. When all seats are sold, the revenue is $26,400. If the number of box seats is one-third the number of bleacher seats, how many seats of each type are there?
7. Business Tickets to a band concert cost $5 for adults, $3 for teenagers, and $2 for preteens. There were 570 people at the concert, and total ticket receipts were $1950. Three-fourth as many teenagers as preteens attended. How many adults, teenagers, and preteens attended?
8. Shipping charges at an online bookstore at $4 for 1 book, $6 for 2 books and $7 for three to five books. Last week there were 6400 orders of five or fewer books, and total shipping charges for these orders were $33,600. The number of shipments with $7 charges was 1000 less than the number with $6 charges. How many shipments were made in each category?
10. Finance Kate borrows $10000, some from her friends at 8% annual interest, twice as much as that from her bank at 9%, and the remainder from her insurance company at 5%. She pays a total of $830 in interest for the first year. How much did she borrow form each source?
11. Business Pretzels cost$3 per lb, dried fruit $4 per pound, and nuts $8 per pound. How many pounds of each should be used to produce 140 pounds of trail mix costing $6 per pound in which there are twice as many pretzels (by weight) as dried fruit?
24. Business An electronics company produces transistors, resistors and computer chips. Each transistor requires 3 units of copper, 1 unit of zinc, and 2 units of glass. Each resistor requires 3, 2
and 1 units of the three materials, and each computer chip requires 2, 1, and 2 units of these materials, respectively. How many of each product can be made with the following amount of materials?
(a) 810 units of copper, 410 of zinc, and 490 of glass
(b) 765 units of copper, 385 of zinc, and 470 of glass
(c) 1010 units of copper, 500 of zinc, and 610 of glass
32. Management There are three convenience stores in Gambier. This week, Store I sold 88 loaves of bread, 48 quarts of milk, 16 jars of peanut butter and 112 pounds of cold cuts. Store II sold 105 loaves
of bread, 72 quarts of milk, 21 jars of peanut butter, and 147 pounds of cold cuts. Store III sold 60 loaves of bread, 40 quarts of milk, no peanut butter, and 50 pounds of cold cuts.
(a) Use a 3 4 matrix to express the sales information for the three stores.
(b) During the following week, sales on these products increased by 25%; sales at Store II increase by
One-third, and sales at Store III increased by 10%. Write the sales matrix for that week.
(c) Write a matrix that represents total sales over the two-week period.
54. Business Burger Barn's three locations sell hamburgers, fries, and soft drinks. Barn I sells 900 burgers, 600 orders of fries, and 750 soft drinks each day. Barn II sells 1500 burgers a day and Barn III sells 1150. Soft drink sales number 900 a day at Barn II and 825 a day at Barn III. Barn II sells 950 orders of fries per day and Bam III sells 800.
(a)Write a 3 3 matrix S that displays daily sales figures for all locations.
(b)Burgers cost $1.50 each, fries $.90 an order, and soft drinks $.60 each. Write a 1 3 matrix P that displays the prices.
(c) What matrix product displays the daily revenue at each of the three locations?
(d)What is the total daily revenue from all locations?