Comparing Two Shipping Quotes with Weight Breaks
A warehouse must ship 14 identical cartons. Each carton weighs 38 pounds and measures 24 × 18 × 12 inches. Carrier X charges by actual weight with a rate of $0.42 per pound for the first 500 pounds and $0.31 per pound for every pound above 500. Carrier Y charges by dimensional weight (L×W×H ÷ 166, rounded up to the next whole pound) at a flat $0.55 per pound, but caps any single shipment at $900. A fuel surcharge of 9% applies to whichever base charge is lower, added on top of that carrier's base only. The shipper also has a $75 pickup fee that is waived if total shipment weight exceeds 600 pounds.
1. Compute the base charge for each carrier before surcharges.
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Actual total weight = 14 × 38 = 532 lb. Carrier X: first 500 lb × $0.42 = $210.00; remaining 32 lb × $0.31 = $9.92; base = $219.92. Carrier Y: dimensional weight per carton = (24×18×12)/166 = 5184/166 = 31.23 → round up to 32 lb. Total dim weight = 14 × 32 = 448 lb. Base = 448 × $0.55 = $246.40 (under the $900 cap).
2. Which carrier is cheaper after the 9% surcharge and any pickup fee, and by how much?
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Carrier X: 219.92 × 1.09 = $239.71. Carrier Y: 246.40 × 1.09 = $268.58. Pickup fee is waived because 532 lb > 600? No - 532 < 600, so the $75 fee applies to both equally. Totals: X = 239.71 + 75 = $314.71; Y = 268.58 + 75 = $343.58. Carrier X is cheaper by $28.87.
3. The shipper can repack to reduce each carton's dimensions. What is the smallest per-carton dimensional weight that would make Carrier Y cheaper than Carrier X on base charge alone?
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Need Y base < X base = $219.92. Per carton: 219.92 ÷ 14 = $15.708, ÷ $0.55 = 28.56 lb per carton, so dim weight must round to ≤ 28 lb. Need L×W×H ÷ 166 ≤ 28, i.e. volume ≤ 28 × 166 = 4648 in³. Current volume is 5184 in³, so cartons must shrink by at least 536 in³ each. Any repack producing ≤ 4648 in³ (dim weight rounding to 28) makes Y's base ≤ 14 × 28 × 0.55 = $215.60, below X's $219.92.