An industrial company manufactures solar batteries. The business has become larg
ID: 3100222 • Letter: A
Question
An industrial company manufactures solar batteries. The business has become large enough fo it to purchase company trucks for product shipments. Each solar battery measures 9 inches in length by 8 inches in width by 10 inch in height. Note: no battery may be turned on its side when shipped. The company must choose one box size and one truck size to complete solar battery shipments.The box supplier provides the company with the following 5 box sizes:
Box 1: 20 inches long by 18 inches wide by 20 inches high
Box 2: 18 inches long by 16 inches wide by 20 inches high
Box 3: 24 inches long by 18 inches wide by 20 inches high
Box 4: 24 inches long by 18 inches wide by 24 inches high
Box 5: 27 inches long by 24 inches wide by 20 inches high
The company may select from 4 trucks with the following cargo dimensions.
Truck 1: 40 ft long by 8 ft wide by 7 ft 6 in high.
Truck 2: 35 ft long by 8 ft wide by 8 ft 4 in high.
Truck 3: 40 ft long by 7 ft 8 in wide by 8 ft 4 in high.
Truck 4: 38 ft 8 in long by 7 ft 6 in wide by 8 ft 4 in high.
Which combination of box size and truck soze would be needed to ship the solar batterriesupright w/o any wasted carg space? Also, how many batteries would be shipped in each shipment considering the the selection of box size and truck size?
Explanation / Answer
Let's start with volume of the battery. V =9*8*10 = 720 in3
Since the battery is 10 inches high we will want a box high 20 inches and not 24 in. So Box 4 is out of the solution since it is 24 inches. The llenght and the width must be divisible by 8 or 9. So box 1 is out since it 20 inches long and it will have space of 2 inches.
We have left box 2, 3 and 5 left to decide.
Box 2 is 18 in long by 16 in wide. It means we can put 8 batteries in it. (4 on the bottom and 4 on top)
Box 3 is 24 in long by 18 in wide. It means that we can put 12 batteries in it.(6 on the bottom and 6 on the top)
Box 5 is 27 in long by 24 in wide. It means that we can put 18 batteries in it. (9 on the bottom and 9 on the top)
So we choose box 5. Its volume is 27*24*20 = 12,960 cubic inches = 7.5 cubic feet
To consider the trucks we need to convert the box dimensions into feet and compare with the truck size if it will fit exactly.
Truck 1 : 40 *8*7.5 = 2,400 cubic feet
Truck 2 : 35* 8* (8 + 4/12) =35 * 8 * (96 +4)/12 =35* 8* 100/12 = 2,333.33 cubic feet
Truck 3 : 40 * (7 + 8/12)* (8 +4/12) = 40* (84+8)/12 * (96+4)/12 = 40 * 92/12 * 100/12 = 2,555.55 cubic feet
Truck 4 : (38 + 8/12)* (7.5) * (8+4/12) = 464/12 *7.5 * 96/12 = 2,320
Now we will divide the volumes by the volume of the box which 7.5 cubic feet to see how many boxes will fit in each one of them.
Truck 1: 2400 /7.5 = 320 boxes
truck 2 : 2333.33/7.5 = 311.111 it is not a whole number so we will disregard it.
Truck 3 : 2,555.55/7.5 = 340.74 not a whole number not an answer
truck 4 : 2320 / 7.5 = 309.33 not a whole number.
So the answer is Truck 1 with 320 boxes and 320*18 = 5760 batteries in it.