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Sagot :
Answer:
- $2300000- max profit
- 5.77 years into operation - zero profit time
Step-by-step explanation:
Given function:
- p(t)= -3t^2 + 18t - 4
It is a quadratic function with general form of y = ax^2 + bx + c
It opens down if a < 0 and gets maximum value at vertex which is determined at x = -b/2a
For the given function vertex is:
- t = -18/-3*2 = 3
Maximum value of p is:
- p(3) = -3*3^2 + 18*3 - 4 = -27 + 54 - 4 = 23 ($2300000)
The time when profit is zero:
- -3t^2 + 18t - 4 = 0
- 3t^2 - 18t + 4 = 0
- t = (18 ± √18² - 4*3*4)/2*3 = (18 ± √276)/6 = (18 ± 16.61)/6
- t = (18 - 16.61)/6 = 0.23 this is the time when company has just started to make profit, it is not applicable as is the past time
- t = (18 + 16.61)/6 = 5.77 years into operation, after this time there will be no profit
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