A manufacturing company has determined that the cost of labor for producing x transmissions is:

L(x) = 0.3x^2 + 400x + 550 dollars,
while the cost of materials is
M(x) = 0.1x^2 + 50x + 800 dollars.

Need to write a polynomial T(x) that represents the total cost of materials and labor for producing x transmissions.

Need to evaluate the total cost of polynomial for x=500

Need to find the cost of labor for 500 transmissions and the cost of materials for 500 transmissions.

(Any help would greatly be appreciated. I really don't understand any of this)

wouldn't

T(x) = L(x) + M(x) , that is, the combined cost of labour and material ?

" Need to evaluate the total cost of polynomial for x=500 "

just replace x with 500 and evaluate

" cost of labor for 500 transmissions "
replace x with 500 in L(x) and evaluate

" cost of materials for 500 transmissions. "
replace x with 500 in M(x) and evaluate

Thank you for your help, I really appreciate it.

welcome

To find the polynomial T(x) that represents the total cost of materials and labor for producing x transmissions, you simply need to add the cost of labor (L(x)) and the cost of materials (M(x)) together.

T(x) = L(x) + M(x)

Now, let's calculate the total cost (T(x)) for x = 500:

Step 1: Calculate the cost of labor for 500 transmissions
To find the cost of labor for 500 transmissions, substitute x = 500 into the labor cost function L(x):
Cost of labor for 500 transmissions = L(500) = 0.3(500)^2 + 400(500) + 550

Step 2: Calculate the cost of materials for 500 transmissions
To find the cost of materials for 500 transmissions, substitute x = 500 into the material cost function M(x):
Cost of materials for 500 transmissions = M(500) = 0.1(500)^2 + 50(500) + 800

Now, let's evaluate these expressions to find the answers.

Cost of labor for 500 transmissions:
Substitute x = 500 into the labor cost function:
L(500) = 0.3(500)^2 + 400(500) + 550
= 0.3(250,000) + 200,000 + 550
= 75,000 + 200,000 + 550
= 275,550 dollars

Cost of materials for 500 transmissions:
Substitute x = 500 into the material cost function:
M(500) = 0.1(500)^2 + 50(500) + 800
= 0.1(250,000) + 25,000 + 800
= 25,000 + 25,000 + 800
= 50,800 dollars

Therefore, the cost of labor for 500 transmissions is 275,550 dollars, and the cost of materials for 500 transmissions is 50,800 dollars.