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The profit (in R1000s) yielded by a company, using a machine that produces bottle caps, is dependent on the average speed at which the machine runs. 

The profit (P) is calculated using the formula:

$$P=-3v^2+30v$$

where $v$ is the average speed (in kilometers per hour) and $v>0$

  1. Calculate the average speed at which neither a profit , nor a loss is yielded.
  2. Determine at what average speed the machine should run so that the maximum profit is obtained.
  3. Hence, or otherwise, calculate the resulting maximum profit.
in Mathematics by Diamond (62,028 points) | 31 views

1 Answer

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1. P =  -3v^2 + 30v
Neither profit nor loss at P = 0
 3v(v -10) = 0
v = 0 or v =10
v = 10 km/hr.

2. P =  -3v^2 + 30v

dP/dv =  -6v + 30 = 0

        v  = 5 km/hr

3. Pmax (in R1000) = 3(5)^2 + 30(5) =  75 (in R1000) or R75 000
by Diamond (42,434 points)

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