.Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock.Betty stocks three brands of beer – Yodel, Shotz, and Rainwater.The cost per gallon (to the tavern owner) of each brand is as follows:
Brand Cost/gallon
Yodel $1.50
Shotz 0.90
Rainwater 0.50
The tavern has a budget of $2,000 for beer for Super Bowl Sunday.Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon.Based on past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and 300 gallons of Rainwater.The tavern has a capacity to stock 1,000 gallons of beer; Betty wants to stock up completely.Betty wants to determine the number of gallons of each brand of beer to order so as to maximize profit.
a. Formulate a linear programming model for this problem (written in a format similar to the way Problems 1 and 2 were presented).
b. Solve this problem by using the computer.
3. Joe Henderson runs a small metal part shop. The shop contains three machines- a drill press, a lathe, and a grinder. Joe has three operators, each certified to work on all three machines. However each operator performs better on some machines than on other. The shop has contracted to do a big job that requires all three machines. The times required by the various operators to perform the required operations on each machine are summarized as follows.
Operator Drill Press (min) Lathe (min) Grinder (min)
1 22 18 35
2 41 30 28
3 25 36 18
Joe Henderson wants to assign one operator to each machine so that the total operating time for all three operators in minimized.
A. Formulate a linear programming model for this problem
B. Solve the model using the computer
C. Joe’s brother, Fred, has asked him to hire his wife, Kelly, who is a machine operator. Kelly can perform each of the three required machine operations in 20 minutes. Should Joe hire his sister-in-law?
16. The athletic boosters club for Beaconville has planned a 2-day fund-raising drive to purchase uniforms for al the local high schools and to improve facilities. Donations will be solicited during the day and night by telephone and personal contact. The boosters club has arranged for local college students to donate their time to solicit donations. The average donation from each type of contact and the time for a volunteer to solicit each type of donations are as follows:
Average donation ($) Average Interview Time (min.)
Phone Personal Phone Personal
Day 16 33 6 13
Night 17 37 7 19
The boosters club has gotten several businesses and car dealers to donate gasoline and cars for the college students to use to make a maximum of 575 personal contacts daily during the fund-raising drive. The college students will donate a total of 22 hours during the day and 43 hours at night during the drive.
The president of the booster club wants to know how many different types of donor contacts to schedule during the drive to maximize the total donations. Formulate and solve an integer program between the integer and non-integer rounded-down solutions to this problem?
Harry and Melissa Jacobson produce handcrafted furniture in a workshop on their farm. They have obtained a load of 600 board feet of birch from a neighbor and are planning to produce round kitchen tables and ladder-back chairs during the next 3 months. Each table will require 30 hours of labor, each chair will require 18 hours, and between them they have a total of 480 hours of labor available. A table requires 40 board feet of wood to make, and a chair requires 15 board feet. A table earns the couple $575 in profit. Most people who buy a table also want four chairs to go with it, so for every table that is produced, at least four chairs must also be made, although additional chairs can also be sold separately. Formulate and solve an integer programming model to determine the number of tables and chairs the Jacobsons should make to maximize profit.
