The total revenue and total cost functions for manufacturing Items are: TR(q)=-5q2+80q and TC(q)=q³-12q²+60q+60, ,2. where a is measured in hundreds of Items and total revenue and total cost are given in hundreds of dollars. (a) Determine the quantity at which marginal revenue is 64 dollars per Thing. q= hundred Items (b) Find the largest interval on which total revenue is increasing. from q= to q= hundred Items (c) Find the largest interval on which profit is increasing. from q= to q= hundred Items (d) What is the largest value of total revenue? hundred dollars (e) What is the marginal revenue at the two quantities at which marginal cost is $39 per Item? MR at smaller quantity: MR at larger quantity: dollars per Item dollars per Item (f) At what quantity does the graph of marginal cost have a horizontal tangent line? (If no such quantity exists, type NONE in the answer blank.) hundred Items (g) At what quantity does the graph of total cost have a horizontal tangent line? (If no such quantity exists, type NONE in the answer blank.) hundred Items (h) True or false? The graph of total cost is always increasing. True False
The total revenue and total cost functions for manufacturing Items are: TR(q)=-5q2+80q and TC(q)=q³-12q²+60q+60, ,2. where a is measured in hundreds of Items and total revenue and total cost are given in hundreds of dollars. (a) Determine the quantity at which marginal revenue is 64 dollars per Thing. q= hundred Items (b) Find the largest interval on which total revenue is increasing. from q= to q= hundred Items (c) Find the largest interval on which profit is increasing. from q= to q= hundred Items (d) What is the largest value of total revenue? hundred dollars (e) What is the marginal revenue at the two quantities at which marginal cost is $39 per Item? MR at smaller quantity: MR at larger quantity: dollars per Item dollars per Item (f) At what quantity does the graph of marginal cost have a horizontal tangent line? (If no such quantity exists, type NONE in the answer blank.) hundred Items (g) At what quantity does the graph of total cost have a horizontal tangent line? (If no such quantity exists, type NONE in the answer blank.) hundred Items (h) True or false? The graph of total cost is always increasing. True False
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The total revenue and total cost functions for manufacturing Items are:
TR(q)=-5q²+80q and TC(q)=q³-12q²+60q+60,
where q is measured in hundreds of Items and total revenue and total cost are given in hundreds of dollars.
(a) Determine the quantity at which marginal revenue is 64 dollars per Thing.
q=
hundred Items
(b) Find the largest interval on which total revenue is increasing.
from q=
to q=
hundred Items
(c) Find the largest interval on which profit is increasing.
from q=
to q=
hundred Items
(d) What is the largest value of total revenue?
hundred dollars
(e) What is the marginal revenue at the two quantities at which marginal cost is $39 per Item?
MR at smaller quantity:
dollars per Item
dollars per Item
MR at larger quantity:
(f) At what quantity does the graph of marginal cost have a horizontal tangent line? (If no such quantity exists, type NONE in the answer blank.)
hundred Items
(g) At what quantity does the graph of total cost have a horizontal tangent line? (If no such quantity exists, type NONE in the answer blank.)
hundred Items
(h) True or false?
The graph of total cost is always increasing.
O True
O False
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