Question

A 4-billion-bushel corn crop brings a price of $2.4/bushel. A commodity broker uses the following rule of thumb: If the crop is reduced by x percent, then the price increases by 10x cents. Which crop size results in maximum revenue and what is the price per bushel? Revenue is equal to price times crop size. (Use decimal notation. Give your answers to two decimal places.) crop size__________.billion bushels price per bushel___________.$

Answer 1

Answer:

Step-by-step explanation:

The second crop size results in maximum revenue. The price per bushel of the second crop size is 3.54 dollars.

Step-by-step explanation: FIRST: Ensure all figures for price are in the same unit (same for quantity)

Hence, 10X cents = 0.1X dollars

SECOND:

Derive the equations for the new price and new quantity

P2 = P1 + 0.1X

Q2 = Q1 - (X% of Q1)

THIRD:

Input the values of Q1 and P1 into the equations

FOURTH:

To get X, equate P2 to Q2

P2 = Q2

From here, X = 11.4286

FIFTH:

Use this value of X to find the values of Q2 and P2 which will be 3.543 billion bushels and 3.54286 dollars respectively.

SIXTH:

The new revenue will now be 12.55 billion dollars which is obviously higher than the initial revenue of 9.6 billion dollars. Remember that R=P.Q

Revenue= Price x Quantity