846 CHAPTER 11 Systems of Equations and Inequalities 75% lean ground beef 60% lean ground pork 70% lean meat loaf 26. Ice Cream The Mom and Pop Ice Cream Company makes two kinds of chocolate ice cream: regular and premium. The properties of 1 gallon (gal) of each type are shown in the table: Flavoring Milk-fat products Shipping weight Profit 20 oz 20 oz 6 lbs $0.90 24 oz 12 oz 5 lbs $0.75 Regular Premium In addition, current commitments require the company to make at least 1 gal of premium for every 4 gal of regular. Each day, the company has available 725 pounds (lb) of flavoring and 425 lb of milk-fat products. If the company can ship no more than 3000 lb of product per day, how many gallons of each type should be produced daily to maximize profit? Source: www.scitoys.com/ingredients/ice_cream.html 27. Maximizing Profit on Ice Skates A factory manufactures two kinds of ice skates: racing skates and figure skates. The racing skates require 6 work-hours in the fabrication department, whereas the figure skates require 4 work-hours there. The racing skates require 1 work-hour in the finishing department, whereas the figure skates require 2 work-hours there. The fabricating department has available at most 120 work-hours per day, and the finishing department has no more than 40 work-hours per day available. If the profit on each racing skate is $10 and the profit on each figure skate is $12, how many of each should be manufactured each day to maximize profit? (Assume that all skates made are sold.) 28. Financial Planning Ariana became a contestant on a game show and ended up winning second prize, which paid $5000. She decides to invest the money. The financial adviser suggests two securities: an AAA bond that yields 8% per annum and a certificate of deposit (CD) that yields 4%.After careful consideration of the alternatives, Ariana decides to invest at most $2000 in the AAA bond and at least $1500 in the CD. She also instructs the financial adviser to invest at least as much in the CD as in the AAA bond. How should the financial adviser proceed to maximize the return on Ariana’s investment? 29. Product Design An entrepreneur is having a design group produce at least six samples of a new kind of fastener that he wants to market. It costs $9.00 to produce each metal fastener and $4.00 to produce each plastic fastener. He wants to have at least two of each version of the fastener and needs to have all the samples 24 hours (h) from now. It takes 4 h to produce each metal sample and 2 h to produce each plastic sample. To minimize the cost of the samples, how many of each kind should the entrepreneur order? What will be the cost of the samples? The farmer cannot spend more than $1800 in preparation costs and cannot use a total of more than 120 workdays. How many acres of each crop should be planted to maximize the profit? What is the maximum profit? What is the maximum profit if the farmer is willing to spend no more than $2400 on preparation? 21. Banquet Seating A banquet hall offers two types of tables for rent: 6-person rectangular tables at a cost of $28 each and 10-person round tables at a cost of $52 each. Kathleen would like to rent the hall for a wedding banquet and needs tables for 250 people. The hall can have a maximum of 35 tables, and the hall has only 15 rectangular tables available. How many of each type of table should be rented to minimize cost and what is the minimum cost? Source: facilities.princeton.edu 22. Spring Break The student activities department of a community college plans to rent buses and vans for a springbreak trip. Each bus has 40 regular seats and 1 special seat designed to accommodate travelers with disabilities. Each van has 8 regular seats and 3 special seats. The rental cost is $350 for each van and $975 for each bus. If 320 regular and 36 special seats are required for the trip, how many vehicles of each type should be rented to minimize cost? Source: www.busrates.com 23. Return on Investment An investment broker is instructed by her client to invest up to $20,000, some in a junk bond yielding 9% per annum and some in Treasury bills yielding 7% per annum. The client wants to invest at least $8000 in T-bills and no more than $12,000 in the junk bond. (a) How much should the broker recommend that the client place in each investment to maximize income if the client insists that the amount invested in T-bills must equal or exceed the amount placed in the junk bond? (b) How much should the broker recommend that the client place in each investment to maximize income if the client insists that the amount invested in T-bills must not exceed the amount placed in the junk bond? 24. Production Scheduling In a factory, machine 1 produces 8-inch (in.) pliers at the rate of 60 units per hour (h) and 6-in. pliers at the rate of 70 units h. Machine 2 produces 8-in. pliers at the rate of 40 units h and 6-in. pliers at the rate of 20 units h. It costs $50 h to operate machine 1, and machine 2 costs $30 h to operate. The production schedule requires that at least 240 units of 8-in. pliers and at least 140 units of 6-in. pliers be produced during each 10-h day. Which combination of machines will cost the least money to operate? 25. Managing a Meat Market A meat market combines ground beef and ground pork in a single package for meat loaf. The ground beef is 75% lean (75% beef, 25% fat) and costs the market $2.25 per pound (lb). The ground pork is 60% lean and costs the market $1.35 lb. The meat loaf must be at least 70% lean. If the market wants to make at least 180 lb of meat loaf by using at least 50 lb of its available pork, but no more than 200 lb of its available ground beef, how much ground beef should be mixed with ground pork so that the cost is minimized?
RkJQdWJsaXNoZXIy NjM5ODQ=