Ace manufacturing has determined that the cost of labor for producing x transmissions is
L(x) = 0.3x2 + 400x + 550 dollars,
While the cost of materials is
M(x) = 0.1x2 + 50x + 800 dollars.
Write a polynomial T(x) that represents the total cost of materials and labor for producing x transmissions.
Evaluate the total cost polynomial for x =500.
Find the cost of labor for 500 transmissions and the cost of materials for 500 transmissions.
Any and all help would be greatly appreciated! I am totally confused.
To find the polynomial T(x) that represents the total cost of materials and labor for producing x transmissions, you add the cost of labor (L(x)) and the cost of materials (M(x)):
T(x) = L(x) + M(x)
Substituting the given expressions for L(x) and M(x), we have:
T(x) = (0.3x^2 + 400x + 550) + (0.1x^2 + 50x + 800)
Simplifying T(x), we combine like terms:
T(x) = 0.3x^2 + 0.1x^2 + 400x + 50x + 550 + 800
T(x) = 0.4x^2 + 450x + 1350
So, the polynomial T(x) representing the total cost of materials and labor for producing x transmissions is 0.4x^2 + 450x + 1350.
To evaluate the total cost polynomial for x = 500, we substitute x = 500 into T(x):
T(500) = 0.4(500^2) + 450(500) + 1350
T(500) = 0.4(250000) + 225000 + 1350
T(500) = 100000 + 225000 + 1350
T(500) = 326350
The total cost of producing 500 transmissions, according to the given polynomial, is $326350.
To find the cost of labor for 500 transmissions, we substitute x = 500 into the labor cost polynomial, L(x):
L(500) = 0.3(500^2) + 400(500) + 550
L(500) = 0.3(250000) + 200000 + 550
L(500) = 75000 + 200000 + 550
L(500) = 276550
The cost of labor for producing 500 transmissions, according to the given polynomial, is $276550.
To find the cost of materials for 500 transmissions, we substitute x = 500 into the materials cost polynomial, M(x):
M(500) = 0.1(500^2) + 50(500) + 800
M(500) = 0.1(250000) + 25000 + 800
M(500) = 25000 + 25000 + 800
M(500) = 50800
The cost of materials for producing 500 transmissions, according to the given polynomial, is $50800.