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

The correct answer is option b)

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

Step-by-step 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

....... (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

....... (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

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step-by-step explanation:

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