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 A distributor of apple juice has 5000 bottle in the store that it wishes to distribute in a month. From experience it is known that demand D (in number of bottles) is given by D= -2000p2+2000p+17000. The price per bottle that will result zero inventory is
  • a)
    Rs. 3
  • b)
    Rs. 5
  • c)
    Rs. 2
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A distributor of apple juice has 5000 bottle in the store that it wish...
Solution:

Given, the demand function is D= -2000p2 +2000p +17000.

To find the price per bottle that will result in zero inventory, we need to find the price at which demand equals 5000 bottles.

Step 1: Equate demand to 5000 and solve for p.

D = 5000

5000 = -2000p2 +2000p +17000

Step 2: Simplify the equation.

0 = -2000p2 +2000p +12000

0 = -2p2 +2p +12

0 = -p2 + p + 6

Step 3: Solve the quadratic equation.

Using the quadratic formula, we get:

p = (-b ± √(b2 - 4ac)) / 2a

Where a = -1, b = 1, and c = 6.

p = (-1 ± √(12)) / -2

p = (-1 ± 3.464) / -2

p = 2.732 or -1.732

Step 4: Check for extraneous root.

The negative root is extraneous since it does not make sense in the context of the problem.

Step 5: Final answer.

Therefore, the price per bottle that will result in zero inventory is Rs. 3 (approx).
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Community Answer
A distributor of apple juice has 5000 bottle in the store that it wish...
Here D=5000 as inventory =0
substitute P=3 in the given equation 
we get D =5000 so ans=3 

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A distributor of apple juice has 5000 bottle in the store that it wishes to distribute in a month. From experience it is known that demand D (in number of bottles) is given by D= -2000p2+2000p+17000. The price per bottle that will result zero inventory isa)Rs. 3b)Rs. 5c)Rs. 2d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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