Cost, revenue, and profit: For a certain manufacturer, revenue has been increasi
ID: 3017828 • Letter: C
Question
Cost, revenue, and profit: For a certain manufacturer, revenue has been increasing but so has the cost of materials and the cost of employee benefits. Suppose revenue can be modeled by , the cost of materials by M(t) = 2t + 1, and the cost of benefits by C(t) = 0.1t2 + 2, where t represents the number of months since operations began and outputs are in thousands of dollars. Use this information to complete the following.
Find the function that represents the total manufacturing costs.
Find the function that represents how much more the operating costs are than the cost of materials.
What was the cost of operations in the 10th month after operations began?
How much less were the operating costs than the cost of materials in the 10th month?
Find the function that represents the profit earned by this company.
Find the amount of profit earned in the 5th month and 10th month. Discuss each result.
Explanation / Answer
Given the cost of materials is M (t) = 2t+1
Cost of employee benefits C (t) = 0.1t^2 + 2
in thousand dollars.
Where t is in months wince operation began.
1.Function representing total manufacturing cost = cost of materials + cost of benefits.
Let it be S (t) = C (t)+ M (t)
S (t) = 0.1t^2+2t+3
2.function representing the operating cost more than cost of materials
N (t) = M (t) -c (t)
=2t+1 - (0.1t^2+2)
=-0.1t^2+2t-1
3.cost of operations in 10th month after operation began
M (t) = M (10) = 0.1× 10^2 +2
=12 thousand dollars.
4.operation costs less than materilas in 10th month
M (10)-C (10)
=12-2 (10)+1
12-21
9 thousand dollars
For writing profit function we need Revenue function