A businesman is considering opening a small specialized trucking firm. To make t
ID: 2943275 • Letter: A
Question
A businesman is considering opening a small specialized trucking firm. To make the firm profitable, it is estimated that it must have a daily trucking capacity of at least 84,000 cu.ft. The type of truck appropriate for this specialized operation comes in two sizes - small and large. The small truck has a capacity of 2,400 cu. ft. and only 1 driver is needed. The large truck has a capacity of 6,000 cu.ft. and 3 drivers are required for the long haul trips. The small truck cost $18,000 and the large truck is $45,000. There are 41 potential drivers available and there are facilities for at most 40 trucks.a) Formulate this as an LP problem to minimize cost. Write out the decision variables, objective and constraints.
b) Use "The Management Scientist" to solve. What is the solution? What will be the total cost?
c) Due to the recent increase in gas prices, the businessman estimates that he will need an extra 10,000 cu. ft. capacity per day to make the firm profitable. By how much would this increase the cost? Is this within limits?
Explanation / Answer
which one are the counstrint because i knid a little bit confuse!!!!!!!! where the 5L+2S>=70 came from!!!!!!!!!!
CONSTRAINTS ARE GIVEN UNDER THE HEAD CONSTRAINTS ..HIGHLIGHTING BELOW IN RED ..
THEY ARE NUMBERED 1,2,3..
SUBSEQUENTLY I MENTIONED UNDER NOS.5 AND 6 ...PHYSICAL CONSTRINTS LIKE WE CAN NOT HAVE
NEGATIVE NUMBER OF SMALL OR LARGE TRUCKS, THOUGH MATHEMATICALLY IT CAN BE CONSIDERED.
THEY ARE IMPLIED PHYSICAL CONSTRINTS IN ALL PROBLEMS NOT USUALLY MENTIONED , BUT UNDERSTOOD AS OBVIOUS.
5L+2S>=70 came FROM THE GIVEN CONSTRAINT...
TOTAL CAPACITY AVAILABLE =
6000L+2400S >=84000
DIVIDING THROUGH OUT WITH 1200 THIS GETS SIMPLIFIED TO
5L+2S>=70
=======================
Question Details
A businesman is considering opening a small specialized trucking firm. To make the firm profitable, it is estimated that it must have a daily trucking capacity of at least 84,000 cu.ft. The type of truck appropriate for this specialized operation comes in two sizes - small and large. The small truck has a capacity of 2,400 cu. ft. and only 1 driver is needed. The large truck has a capacity of 6,000 cu.ft. and 3 drivers are required for the long haul trips. The small truck cost $18,000 and the large truck is $45,000. There are 41 potential drivers available and there are facilities for at most 40 trucks.
a) Formulate this as an LP problem to minimize cost. Write out the decision variables, objective and constraints.
b) Use "The Management Scientist" to solve. What is the solution? What will be the total cost?
c) Due to the recent increase in gas prices, the businessman estimates that he will need an extra 10,000 cu. ft. capacity per day to make the firm profitable. By how much would this increase the cost? Is this within limits?
LET THE NUMBER OF LARGE TRUCKS BE = L........DECISION VARIABLES ARE L AND S
LET THE NUMBER OF SMALL TRUCKS BE = S
DECISION VARIABLES ARE L AND S
CONSTRAINTS
TOTAL NO.OF TRUCKS =
L+S<=40...............................................................1
TOTAL CAPACITY AVAILABLE =
6000L+2400S >=84000
5L+2S>=70....................................2
DRIVERS NEEDED IS
3L+1S<=41.............................................................3
TOTAL COST = P
P= 45000L+18000S................................4....OBJECTIVE .....
L>=0.........................................5
S>=0............................................6)
b) Use "The Management Scientist" to solve. What is the solution? What will be the total cost?
OPTIMUM OCCURS AT ONE OF THE VERTICES OF POLYGON ABC
SEE FIGURE....A[5,12] IS INTERSECTION OF 2 AND 3
B[35,0] IS INTERSECTION OF 2 AND 6
C IS [41,0]
AT A[5,12]....COST IS
P= 45000L+18000S................................4....OBJECTIVE
P=45000*5+18000*12 = 441000
AT B[35,0]..COST IS
P=18000*35 =630000
AT C[41,0]...COST IS
P=18000*41=738000
HENCE A IS THE BEST SOLUTION ....
SO 5 SMALL TRUCKS AND 12 LARGE TRUCKS ARE TO BE BOUGHTAT A TOTAL COST OF
c) Due to the recent increase in gas prices, the businessman estimates that he will need an extra 10,000 cu. ft. capacity per day to make the firm profitable. By how much would this increase the cost? Is this within limits?
EQN.2 WILL CHANGE ..
FROM
6000L+2400S >=84000
5L+2S>=70....................................2
TO
6000L+2400S >=91000
60L+24S>=91...............................2 ALTERED...
FIND OUT A,B,C AGAIN AS ABOVE AND FIND THE OPTIMUM COST AS OUT LINED ABOVE
HOPE YOU CAN DO IT
IF IN DIFFICULTY PLEASE COME BACK
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.