A truck company has $800,000 to pruchase new vehicles. Vehicle A: 10 ton pay-loa

Question

A truck company has $800,000 to pruchase new vehicles.

Vehicle A: 10 ton pay-load, 45 mph average speed, cost is $26,000.

Vehicle B: 20 ton pay-load, 40 mph average speed, cost is $36,000.

Vehicle C: 18 ton pay-load, 40 mph average speed, cost is $42,000.

Also,

Vehicle A: requires crew of 1 driver, driven in three shifts a day, operated for an average 18 hr/day

Vehicle B: requres crew of 2 drivers, driven three shifts a day, operated for an average 18 hr/day

Vehicle C: requires crew of 2 drivers, driven three shifts a day, operated for an average 21 hr/day

TOtal number of vehicles must not exceed 30.

driver can only work one shift a day.

Formulate a mathematical model to help determine the number of each type of vehicle the company should purchase to maximize theshipping capacity in ton-miles per day?

Explanation / Answer

Let the number of vehicles purchased of type A, B and C be 'x', 'y' and 'z' respectively

The shipping capacity in ton-miles per day needs to be maximized. For a vehicle, the shipping capacity may be calculated as follows :

Shipping capacity of 1 vehicle per day (in ton-miles) = (Payload (in tons)) * (Average speed (in mph)) * (Average operating time per day (in hrs))

The objective function F, which needs to be maximized becomes :

Maximize F = (10*45*18)x + (20*40*18)y + (18*40*21)z

Objective Function : Maximize F = 8100x + 14400y + 15120z ....(i)

The constraints under which this objective function is to be maximized are :

1. Maximum amount of money available : $800,000

26000x + 36000y + 42000z <= 800000 ...(ii)

2. Maximum number of vehicles to be accomodated : 30

x + y + z <= 30 ....(iii)

3. Non-negativity constraints

x >=0 , y >= 0 , z >= 0 ....(iv)

Thus, the mathematical model to be optimized becomes :

Maximize F = 8100x + 14400y + 15120z, subject to the constraints

26000x + 36000y + 42000z <= 800000 ....(i)

x + y + z <= 30 ....(ii)

x >=0 , y >= 0 , z >= 0 ....(iii)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.