Question

Two kinds of crated cargo, A and B, are to be shipped by truck. Each crate of cargo A is 50 cubic feet in volume and weighs 200 pounds, whereas each crate of cargoB is 10 cubic feet in volume and weighs 360 pounds. The shipping company charges $75 per crate for cargo A and $100 per crate for cargo B. The truck has a maximum load limit of 7200 pounds and 1000 cubic feet. Write a system of inequalities that represent the constraints in this problem.

a. 50a+10b> 7200; 200a+360b> 1000; a> 0; b>0
b. 50a+10b<1000; 200a+360b < 7200; a> 0; b>0
c. 50a+10b7200; 200a +360b < 1000; a s 0; b< 0
d. 50a+ 10b> 1000; 200a+360b> 7200; a s 0; b<0

Answer 1

The correct answer is option b)

50a+10b<1000; 200a+360b < 7200; a> 0; b>0

Explanation:

We are given that Two kind of crated cargo namely A and B to be shipped by truck.

Cargo A:

Volume of each crate of cargo A = 50 cubic ft

Weight of each crate of cargo A = 200 pounds

Let number of crates of cargo A to be shipped = a

Total volume of 'a' crates of cargo A = 50a cubic ft

Total weight of 'a' crates of cargo A = 200a pounds

Cargo B:

Volume of each crate of cargo B = 10 cubic ft

Weight of each crate of cargo B = 360 pounds

Let number of crates of cargo B to be shipped = b

Total volume of 'b' crates of cargo B = 10b cubic ft

Total weight of 'b' crates of cargo B = 360b

Total volume allowed in the truck is 1000 cubic ft

Total volume of 'a' crates of Cargo A and Total volume of 'b' crates of Cargo B = 50a+10b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)

So, the inequality becomes

`50a+10b<1000` ....... (1)

Total weight allowed (load limit) in the truck is 7200 pounds

Total weight of 'a' crates of Cargo A and Total weight of 'b' crates of Cargo B = 200a+360b cubic ft (This sum should be less than volume of truck so that it can fit in the truck)

So, the inequality becomes

`200a+360b<7200 ...... (2)` ....... (1)

And number of crates of cargo A and B are always a positive number.

So, a > 0 and b > 0.

So, the correct answer is option b.

b. 50a+10b<1000; 200a+360b < 7200; a> 0; b>0