21 Truckloads - cost R 498 200

327 - Pallets on the 21 loads - 1 Pallet is 80 boxes p/pallet

160 - Pallets on the 21 loads - 1 pallet is 70 Boxes p/pallet

How much did each diffrent pallet cost on all 21 loads -

1. how much did each of the 327 pallets cost

2. how much did each of the 160 pallets cost

what is the calculation formula to be used
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1 Answer

I hope I've interpreted this question correctly. There seem to be two types of pallet: type A holds 80 boxes per pallet; type B holds 70 boxes per pallet. If each box costs the same then we have 327×80+160×70=37360 boxes altogether. There are 327 type A and 160 type B pallets distributed between the 21 loads.

So 21 truckloads carry 37360 boxes altogether, total cost R498200. Therefore 1 box costs 498200/37360=R13.34 approx (could be written R13,34).

Type A pallet costs 80×13.34=R1066.81 approx (could be written R1 066,81).

Type B pallet costs 70×13.34=R933.46 approx (could be written R933,46).

Best not to think in terms of formulas, just use logic and basic arithmetic. The common unit in this question is the box, because (I assume) each box costs the same, but, because of the different numbers of boxes on each pallet, the cost of the two types of pallet differ. So we start with the fixed cost of a box, determine how many boxes so that we can work out the cost of a single box. Then, knowing how many boxes there are on each pallet, it's possible to work out the cost of each type of pallet. Note that the number of truckloads (21) doesn't come into the calculation. The number of pallets on each truck has to be a whole number and we don't have any details of how the pallets are distributed between the trucks and the question doesn't require that info.

ADDENDUM (not asked for in the question)

We can bring the 21 trucks into the question by load optimisation, that is, how many pallets to load on to the trucks so that each truck has a more or less equal share of the total shipment.

It turns out that one solution is that 17 trucks carry 23 pallets while 4 trucks carry 24 pallets:

17×23+4×24=391+96=487 pallets. This corresponds to the total number of pallets=327+160=487.

The breakdown is:

9 trucks each carry 15 type A (327) pallets (1200 boxes) and 8 type B (160) pallets (560 boxes). Total: 207 mixed pallets, 15,840 boxes. 1 truckload=1760 boxes.

8 trucks each carry 16 type A (327) pallets (1280 boxes) and 7 type B (160) pallets (490 boxes). Total: 184 mixed pallets, 14,160 boxes. 1 truckload=1770 boxes.

4 trucks each carry 16 type A pallets (1280 boxes) and 8 type B pallets (560 boxes). Total: 96 mixed pallets, 7,360 boxes. 1 truckload=1840 boxes.

21 trucks carry a total of 207+184+96=487 pallets, 15840+14160+7360=37,360 boxes. Average truckload=1,790 boxes. Average load based on transporting 37360 boxes=1,779 boxes (approx) per truckload. The two averages are within 1% of each other, which demonstrates that the above distribution of load between 21 trucks is fair. Also, the value of the consignment is also fairly shared between the trucks, varying between R23,470 and R24,537 per truck, average R23,870.

21 trucks carry 160+327=487 pallets, so all pallets have been transported through the shared load.

by Top Rated User (1.1m points)

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