# linear programming

• Dec 11th 2013, 08:57 AM
Mathssub
linear programming
hi all just wondering if you could assist me with the following question

there are two types of boxes. light boxes which weigh 120kg and heavy boxes which weigh 170kg. a truck can carry at most 3890 kg. the time taken to load a heavy box is 7 minutes. the time taken to load a light box is 6 minutes. the total time spent loading a truck cannot be greater then 177 minutes.

a) taking x as the number of heavy boxes and y as the number of light boxes, model two linear inequalities in x and y
b) what values of x and y lead to the most efficient loading of the truck.
c) the firm pays 82\$ for the loading of the each heavy box and 52\$ for the loading of each light box. if the truck is loaded in the most efficient way possible way from the workers point of view what will their income be?
• Dec 11th 2013, 10:41 AM
HallsofIvy
Re: linear programming
Quote:

Originally Posted by Mathssub
hi all just wondering if you could assist me with the following question

there are two types of boxes. light boxes which weigh 120kg and heavy boxes which weigh 170kg. a truck can carry at most 3890 kg. the time taken to load a heavy box is 7 minutes. the time taken to load a light box is 6 minutes. the total time spent loading a truck cannot be greater then 177 minutes.

a) taking x as the number of heavy boxes and y as the number of light boxes, model two linear inequalities in x and y

The heavy boxes weigh a total of 170x kg and the light boxes weigh a total of 120y kg which must be less than or equal to 3890 kg
The heavy boxes take a total of 7x minutes to load and the light boxes take a total of 6y minute which must be less than or equal to 177 min.

Quote:

b) what values of x and y lead to the most efficient loading of the truck.
I presume that "most efficient" means fastest loading so you want to minimize $7x+ 6y\le 177$ subject to $170x+ 120y\le 3890$

Quote:

c) the firm pays 82\$ for the loading of the each heavy box and 52\$ for the loading of each light box. if the truck is loaded in the most efficient way possible way from the workers point of view what will their income be?
Having determined x and y in (b), find 82x+ 52y.