Assume that the demand function for tuna in a small coastal town is given by p = 20,000/q1.5 (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 that the town’s fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month. b. Calculate the monthly revenue R as a function of the number of pounds of tuna 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, and interpret the results.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Assume that the demand function for tuna in a small coastal town is given by
p = 20,000/q1.5 (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 that the town’s fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month.
b. Calculate the monthly revenue R as a function of the number of pounds of tuna 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, and interpret the results.
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 in order to increase its revenue?
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