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The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?
- a)5
- b)4
- c)7
- d)6
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The variable cost (V) of manufacturing a product varies according to t...
Checking with all options in formula: (4q+100/q) i.e. (V+F). Option A gives the minimum cost.
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The variable cost (V) of manufacturing a product varies according to t...
The total cost (TC) is the sum of the variable cost (V) and the fixed cost (F). To minimize the total cost, we need to find the quantity (q) that minimizes the total cost.
The equation for the variable cost is given as V = 4q. This means that for each unit produced, the variable cost is 4 times the quantity produced.
The equation for the fixed cost is given as F = 100/q. This means that as the quantity produced increases, the fixed cost decreases.
To find the total cost, we can substitute the equations for the variable cost and the fixed cost into the equation for the total cost:
TC = V + F
= 4q + 100/q
To minimize the total cost, we can take the derivative of the total cost with respect to q and set it equal to zero:
d(TC)/dq = 4 - 100/q^2 = 0
Solving this equation, we get:
4 = 100/q^2
q^2 = 100/4
q^2 = 25
q = ±5
Since the quantity produced cannot be negative, the only valid solution is q = 5.
Therefore, to minimize the total cost, 5 units should be produced.
Answer: a) 5
The equation for the variable cost is given as V = 4q. This means that for each unit produced, the variable cost is 4 times the quantity produced.
The equation for the fixed cost is given as F = 100/q. This means that as the quantity produced increases, the fixed cost decreases.
To find the total cost, we can substitute the equations for the variable cost and the fixed cost into the equation for the total cost:
TC = V + F
= 4q + 100/q
To minimize the total cost, we can take the derivative of the total cost with respect to q and set it equal to zero:
d(TC)/dq = 4 - 100/q^2 = 0
Solving this equation, we get:
4 = 100/q^2
q^2 = 100/4
q^2 = 25
q = ±5
Since the quantity produced cannot be negative, the only valid solution is q = 5.
Therefore, to minimize the total cost, 5 units should be produced.
Answer: a) 5
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The variable cost (V) of manufacturing a product varies according to the equation V= 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?a)5b)4c)7d)6Correct answer is option 'A'. Can you explain this answer?
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