LINEAR PROGRAMMING
PROJECT
AN EXAMPLE
WORKING PART TIME JOBS
RORY WORKS TWO PART TIME JOBS, AT AN ANIMAL SHELTER AND AS A LIFE
GUARD. HE MAKES $5 AN HOUR AT THE ANIMAL SHELTER AND $8 AN HOUR AS A
LIFE GUARD. HE MUST WORK AT LEAST 2 HOURS A WEEK AT THE ANIMAL SHELTER
TO KEEP HIS JOB. HE ONLY LIFEGUARDS ON SATURDAYS AND HIS LIFEGUARDING
SHIFTS RANGE FROM ZERO TO SIX HOURS EACH WEEK. RORY’S PARENTS REQUIRE
THAT HE WORKS NO MORE THAN 12 HOURS A WEEK.
RORY WANTS TO MAXIMIZE HIS EARNINGS WHILE STILL FULFILLING THE
REQUIREMENTS OF BOTH HIS JOBS AND HIS PARENTS.
THE VARIABLES
𝑥 = ANIMAL SHELTER HOURS
THAT RORY WORKS
𝑦 = LIFEGUARDING HOURS
RORY WORKS
THE CONSTRAINTS
• HE HAS TO WORK AT LEAST TWO HOURS AT THE ANIMAL SHELTER TO MAINTAIN
HIS JOB.
•
𝑥≥2
• HE WORKS BETWEEN ZERO AND SIX HOURS AT THE POOL ON SATURDAYS.
•
0≤𝑦≤6
• HE CAN ONLY WORK A TOTAL OF 12 HOURS PER WEEK ACCORDING TO HIS
PARENTS.
•
𝑥 + 𝑦 ≤ 12
THE GRAPH AND
THE VERTICES
•
(2,6)
•
(6,6)
•
(2,0)
•
(12,0)
A
C
B
D
OBJECTIVE FUNCTION AND CRITICAL POINTS
Rory wants to work within his constraints to make as much
money as possible. He can make $5 at the animal shelter and
$8 as a life guard.
𝒇(𝒙, 𝒚) = 𝟓𝒙 + 𝟖𝒚
Vertex
A
B
C
D
Coordinates
(2,6)
(6,6)
(2,0)
(12,0)
Money
Earned
$58
$78
$10
$60
CONCLUSION
RORY SHOULD WORK SIX HOURS AT
EACH JOB TO MAXIMIZE HIS EARNINGS.
IF HE DOES THIS HE WILL BE ABLE TO
MAKE
$78 EACH WEEK.