Answer:
The company has to produce more than 92 guitars and sell them for making a profit.
Step-by-step explanation:
These are the cost and revenue functions, where x represents the number of guitars to be manufactured and sold: R(x) = 120x, and C(x) = 100x + 1840.
Therefore, the condition for no loss-no gain for manufacturing x number of guitars is
R(x) = C(x)
⇒ 120x = 100x + 1840
⇒ 20x = 1840
⇒ x = 92
Therefore, the company has to produce more than 92 guitars and sell them for making a profit. (Answer)
Did your explanation include the following?
Some polynomial equations have complex solutions.
Therefore, complex solutions cannot be found by graphing the related system or function in the Cartesian (x-y) plane.
Polynomial functions with all complex solutions do not have x-intercepts, and the related system of equations will not intersect.
The total revenue that is gained from the sales of the cakes is determined by multiplying the number of cakes by the price. If we let x be the number of $1 that should be deducted from the price and y be the total revenue,
y = (25 - x)(100 + 5x)
Simplifying,
y = 2500 + 25x - 5x²
We get the value of x that will give us the maximum revenue by differentiating the equation and equating the differential to zero.
dy/dx = 0 = 25 - 10x
The value of x is 2.5.
The price of the cake should be 25 - 2.5 = 22.5.
Thus, the price of the cake that will give the maximum potential revenue is $22.5.
Answer:
We need 5 bags of Vigoro Ultra Turf and 4 bags of Parkers Premium fertilizer.
Step-by-step explanation:
Let's first list the percentage compositions of each fertilizer type:
<u>Vigoro Ultra Turf:</u>
Nitrogen (N) = 29 kg
Phosphoric Acid (P2O5) = 3 kg
Potash (K2O) = 4 kg
<u>Parkers Premium</u>
Nitrogen (N) = 18 kg
Phosphoric Acid (P2O5) = 25 kg
Potash (K2O) = 6 kg
We can set up simultaneous equations to find out the amount of 100 kg bags of each fertilizer needed:
x = Vigoro Ultra turf (one bag)
y = Parkers Premium (one bag)
29x + 18y = 217 -Equation 1
3x + 25y = 115 -Equation 2
4x + 6y = 44 -Equation 3
Solving for x and y, we get:
x = 5
y = 4
This means we need 5 bags of Vigoro Ultra Turf and 4 bags of Parkers Premium fertilizer.
