Linear Programming Questions!

Hello there!

I am a little stuck on these linear programming questions! I know they're easy but for some reason I just can't get my head around the questions but usually I am fine :/

A wall is to be built using two types of bricks of equal thickness. The wall is to be 3 meters high, 100 meters long and the thickness of a single brick. The large type of a brick is of height 10cm and length 20cm. The small type of brick is of height 5 cm and length 10cm

(i) Ignoring the mortar, the constraint 4L + S => 60,000 ensures there are enough bricks available Identify the variables and explain why it works.

So.. I am assuming that L = large brick and S = small brick.

Height: 10L + 5S = 300 ?
Length: 20L + 10S = 100,000 ?

I know something is wrong as I don't have an inequality!! Any help would be appreciated!

Thanks!

Reply 1

username1560589

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Original post by GingerGnu

Hello there!

I am a little stuck on these linear programming questions! I know they're easy but for some reason I just can't get my head around the questions but usually I am fine :/

A wall is to be built using two types of bricks of equal thickness. The wall is to be 3 meters high, 100 meters long and the thickness of a single brick. The large type of a brick is of height 10cm and length 20cm. The small type of brick is of height 5 cm and length 10cm

(i) Ignoring the mortar, the constraint 4L + S => 60,000 ensures there are enough bricks available Identify the variables and explain why it works.

So.. I am assuming that L = large brick and S = small brick.

Height: 10L + 5S = 300 ?
Length: 20L + 10S = 100,000 ?

I know something is wrong as I don't have an inequality!! Any help would be appreciated!

Thanks!

Work it out using area:
A = 300(10000)
A = 3 x 10⁶

A large brick has four times the area of small brick (5)(10) = (1/4)(10)(20)
The area of a small brick is (5)(10) = 50

At maximum for L, S = 0
At maximum for S, L = 0
(at the maximums all of the bricks are of that kind)

maximum S = (3 x 10⁶)/50 = 60000
maximum L = 60000 / 4

You need at least this area, doesn't matter if you go over
therefore