A small-time farmer decides to sell her home-made yogurt at a farmers market. Sh

Question

A small-time farmer decides to sell her home-made yogurt at a farmers market. She has determined that if she prices her yogurt at $14.00 per pint, she expects to sell 3 pints per hour. However, if she prices her yogurt at $2.00 per pint, she expects to sell 9 pints per hour. She also knows she will have to pay her son $10.00 each hour to man the booth at the market. Based on this information:
A) Construct a linear demand function, relating the price for a pint of yogurt to the quantity sold per hour.
B) Determine the revenue function, as a function of the quantity sold per hour.
C) Determine the profit function, as a function of the quantity sold per hour.
D) Determine the number of pints that need to be sold per hour to maximize the hourly profit.
E) Determine the maximum hourly profit.
F) Determine the price that should be charged for each pint of yogurt to realize the max hourly profit. A small-time farmer decides to sell her home-made yogurt at a farmers market. She has determined that if she prices her yogurt at $14.00 per pint, she expects to sell 3 pints per hour. However, if she prices her yogurt at $2.00 per pint, she expects to sell 9 pints per hour. She also knows she will have to pay her son $10.00 each hour to man the booth at the market. Based on this information:
A) Construct a linear demand function, relating the price for a pint of yogurt to the quantity sold per hour.
B) Determine the revenue function, as a function of the quantity sold per hour.
C) Determine the profit function, as a function of the quantity sold per hour.
D) Determine the number of pints that need to be sold per hour to maximize the hourly profit.
E) Determine the maximum hourly profit.
F) Determine the price that should be charged for each pint of yogurt to realize the max hourly profit.
A) Construct a linear demand function, relating the price for a pint of yogurt to the quantity sold per hour.
B) Determine the revenue function, as a function of the quantity sold per hour.
C) Determine the profit function, as a function of the quantity sold per hour.
D) Determine the number of pints that need to be sold per hour to maximize the hourly profit.
E) Determine the maximum hourly profit.
F) Determine the price that should be charged for each pint of yogurt to realize the max hourly profit.

Explanation / Answer

B. Revenue Function (Rx) = Total income from producing units = $14*3 = $42 (we consider 3 pints per hr @$14)

Revenue Function (Rx) = Total income from producing units = $2*9=$18 (we consider 9 pints per hr @$2)

C. Profit Function (Px) = Total income minus total cost

Px when (we consider 3 pints per hr @$14) is = $42-$10=$32

Px when (we consider 9 pints per hr @$2) is = $18-$10 =$2

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