the cost for operating a commercial truck is knv (1/2) where k is a constant of

Question

the cost for operating a commercial truck is knv (1/2) where k is a constant of proportionality, vis velocity in miles per hour, and n is the trip length in miles. It IS estimated that at 89 mph, the average cost of operation is $5.3 per mile. The truck owner wants to minimize the cost of operation, to do this he needs to balance the operating cost against the cost of delays and unscheduled maintenance, which is assumed to be $10.35 per hour. What i optimal velocity in miles per hour needed to minimize the total costs? (provide answer with one decimal place precision) the

Explanation / Answer

since kv0.5=5.3

for n=1

and v= 89

so k=5.3/(890.5) = 0.56

let the total time be t

so total cost,C = (n/v)*10.35+ k*n*v0.5

so for minimization dC/dv= 0

so dC/dv= -10.35 n/v2+k*n*0.5/v0.5=0

so 10.35= k*0.5*v3/2

putting k=0.56

so v3/2 ? =36.964

v= 11.09655 mph

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.