Suppose a company's demand function is given by p(q)=−0.0475q+30 and p(q) is the price in dollars. Suppose its cost function is given by C(q)=0.13q+1467, where q is number of units sold/produced and C(q) is in dollars. A) What is the Revenue function? R(q) = B) Write an expression for the Profit function. P(q) = C) Find a simplified expression for the marginal profit function. MP(q)=
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.
Suppose a company's demand function is given by p(q)=−0.0475q+30 and p(q) is the price in dollars.
Suppose its cost function is given by C(q)=0.13q+1467, where q is number of units sold/produced and C(q) is in dollars.
A) What is the Revenue function?
R(q) =
B) Write an expression for the Profit function.
P(q) =
C) Find a simplified expression for the marginal profit function. MP(q)=
D) How many items need to be sold to maximize profits?
Answer: units must be sold. (Round to two decimal places.)
E) What is the price that maximizes profit? Express your answer to the nearest penny.
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