Mineral Economics, Mine Planning, Systems Engineering · Systems Engineering · 2 marks · Numerical answer
A truck travelling at x km/h consumes fuel at 20+x²/50 L/hour. Fuel costs₹70/L and other costs₹500/hour. It travels 100 km. Find the speed minimising trip cost in km/h, to one decimal.
Hourly cost is 70(20+x²/50)+500=1900+1.4x² rupees. Trip time is 100/x hours, so trip cost is 190000/x+140x. Set its derivative−190000/x²+140 to zero, giving x=√(190000/140)=36.8394 km/h, or 36.8. The positive second derivative confirms a minimum.
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