a manufacturing company finds that the daily cost of producing x items of Guess jeans is given by C(x)=420x+14000,if each jean is sold for BWP700 find the number that must be sold daily to ensure neither a profit or loss
To find the number of Guess jeans that must be sold daily to neither make a profit nor loss, we need to set the total cost equal to the total revenue.
Let's call the number of jeans that must be sold daily as "n".
The total cost of producing "n" jeans would be:
C(n) = 420n + 14000
The total revenue from selling "n" jeans would be:
R(n) = 700n
Since we want to neither make a profit nor loss, we can set C(n) equal to R(n) and solve for "n":
420n + 14000 = 700n
280n = 14000
n = 50
Therefore, the company must sell 50 Guess jeans daily to ensure neither a profit nor loss.
To determine the number of jeans that must be sold daily to ensure neither a profit nor a loss, we need to find the break-even point. At this point, the total cost (C) is equal to the total revenue (R).
Let's break down the information given:
Cost function: C(x) = 420x + 14000 (where x represents the number of jeans produced/sold daily)
Selling price per jean: BWP700
The revenue is equal to the selling price per jean multiplied by the number of jeans sold: R(x) = 700x.
To find the break-even point, we set the cost equal to the revenue:
C(x) = R(x)
420x + 14000 = 700x
To solve for x, we isolate the variable:
14000 = 700x - 420x
14000 = 280x
Next, we divide both sides of the equation by 280:
14000/280 = x
50 = 50x
x = 50
Therefore, the manufacturing company must sell 50 Guess jeans daily to ensure neither a profit nor a loss.
To ensure neither a profit nor a loss, the revenue from selling the jeans should be equal to the cost of producing them.
The revenue from selling x jeans can be calculated by multiplying the selling price per jeans (BWP700) by the number of jeans sold (x):
Revenue (R(x)) = BWP700 * x
The cost of producing x jeans is given by the function C(x) = 420x + 14000.
Setting the revenue equal to the cost, we have:
BWP700 * x = 420x + 14000
Now we can solve for x:
BWP700x - 420x = 14000
280x = 14000
x = 14000 / 280
x = 50
Therefore, the company must sell 50 Guess jeans daily to ensure neither a profit nor a loss.