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A fuel depot blends premium and regular gasoline to fill a 600-gallon order that must be exactly 92 octane. Premium is 95 octane and regular is 87 octane. The blend is then sold at $4.20 per gallon for the premium portion and $3.60 per gallon for the regular portion. What is the total revenue from the order?
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Correct answer
D
First find the blend split by octane. Let p = premium gallons: (95p + 87(600 − p))/600 = 92 → 95p + 52,200 − 87p = 55,200 → 8p = 3,000 → p = 375, so regular = 225. (Sanity check: 95 is 3 above the 92 target and 87 is 5 below it, so the gallons split 5 : 3 in favor of regular, 375 premium : 225 regular.) Then apply the two prices to the two portions: revenue = 375 × $4.20 + 225 × $3.60 = $1,575 + $810 = $2,385. Both steps are required: the octane weighted-average fixes the split, and only then does the dual-rate pricing give the revenue.
(B) $2,295 swaps the split, pricing 225 gallons as premium and 375 as regular, so the cheaper portion is wrongly treated as the larger one. (C) $2,340 prices all 600 gallons at the simple average $3.90, ignoring that the larger portion is the costlier premium. (A) $2,160 prices everything at the regular $3.60 rate, and (E) $2,520 prices everything at the premium $4.20 rate.
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