Assume that the demand function for tuna in a small coastal town is given by 28,000 р 91.5 (200 ≤ q≤ 800), where p is the price (in dollars) per pound of tuna, and q is the number of pounds of tuna that can be sold at the price p in one month. (a) Calculate the price (in $ per lb) that the town's fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month. per lb (b) Calculate the monthly revenue R (in dollars) as a function of the number of pounds of tuna q. R(q) (c) Calculate the revenue and marginal revenue (derivative of the revenue with respect to q) at a demand level of 400 pounds per month. revenue marginal revenue per lb of tuna Interpret the results. At a demand level of 400 pounds per month, the revenue is $ additional pound of tuna. and decreasing at a rate of $ per (d) If the town fishery's monthly tuna catch amounted to 400 pounds of tuna, and the price is at the level in part (a), would you recommend that the fishery raise or lower the price of tuna to increase its revenue? raise the price lower the price Your monthly profit (in dollars) from your newspaper route is given by P = 4n - √√n where n is the number of subscribers on your route. If you currently have 100 subscribers, find your profit and your marginal profit. profit marginal profit Interpret your answers. per new subscriber Your current profit is $ per month and this would increase at a rate of $ per new subscriber.
Assume that the demand function for tuna in a small coastal town is given by 28,000 р 91.5 (200 ≤ q≤ 800), where p is the price (in dollars) per pound of tuna, and q is the number of pounds of tuna that can be sold at the price p in one month. (a) Calculate the price (in $ per lb) that the town's fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month. per lb (b) Calculate the monthly revenue R (in dollars) as a function of the number of pounds of tuna q. R(q) (c) Calculate the revenue and marginal revenue (derivative of the revenue with respect to q) at a demand level of 400 pounds per month. revenue marginal revenue per lb of tuna Interpret the results. At a demand level of 400 pounds per month, the revenue is $ additional pound of tuna. and decreasing at a rate of $ per (d) If the town fishery's monthly tuna catch amounted to 400 pounds of tuna, and the price is at the level in part (a), would you recommend that the fishery raise or lower the price of tuna to increase its revenue? raise the price lower the price Your monthly profit (in dollars) from your newspaper route is given by P = 4n - √√n where n is the number of subscribers on your route. If you currently have 100 subscribers, find your profit and your marginal profit. profit marginal profit Interpret your answers. per new subscriber Your current profit is $ per month and this would increase at a rate of $ per new subscriber.
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:Assume that the demand function for tuna in a small coastal town is given by
28,000
р
91.5
(200 ≤ q≤ 800),
where p is the price (in dollars) per pound of tuna, and q is the number of pounds of tuna that can be sold at the price p in one
month.
(a) Calculate the price (in $ per lb) that the town's fishery should charge for tuna in order to produce a demand of 400 pounds
of tuna per month.
per lb
(b) Calculate the monthly revenue R (in dollars) as a function of the number of pounds of tuna q.
R(q)
(c) Calculate the revenue and marginal revenue (derivative of the revenue with respect to q) at a demand level of 400 pounds
per month.
revenue
marginal revenue
per lb of tuna
Interpret the results.
At a demand level of 400 pounds per month, the revenue is $
additional pound of tuna.
and decreasing at a rate of $
per
(d) If the town fishery's monthly tuna catch amounted to 400 pounds of tuna, and the price is at the level in part (a), would you
recommend that the fishery raise or lower the price of tuna to increase its revenue?
raise the price
lower the price
Transcribed Image Text:Your monthly profit (in dollars) from your newspaper route is given by
P = 4n - √√n
where n is the number of subscribers on your route. If you currently have 100 subscribers, find your profit and your marginal
profit.
profit
marginal profit
Interpret your answers.
per new subscriber
Your current profit is $
per month and this would increase at a rate of $
per new subscriber.
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