Market Research: You have an apple orchard. You let people pick their own apples. When you...

Market Research:

You have an apple orchard. You let people pick their own apples. When you let people pick a small bag for $6, there were 6,316 small bags sold. You do some market research and find that a $0.25 increase in price means 235 fewer small bags of apples sold. Recall that revenue is quantity sold X Price per quantity. If we let x be the number of $0.25 increases or decreases from $6 and R be revenue, then answer the following questions:

A) What equation represents what you expect the revenue to be based on your research?

B) Based on your answer in A, if you charge $5.75 (x= -1) how much do you expect the revenue to be?

C) At what price or prices will you have $30,000 in sales, If your expectations listed above are true?

I would appreciate any and all help. If you give the answers, could you please show work and explain how you got them? I did my best in trying to re-write the questions (my professor doesnt have great grammar.)

Expert Solution

A). When people are permitted to pick a small bag of apples for $ 6, then 6,316 small bags of apples are sold. The decrease in the no. of small bags of apples sold is 235 when the price per small bag of apples is increased from $ 6 to 6.25. If x be the number of $ 0.25 increases from $ 6 and R be revenue, then the revenue is R= (6+0.25x)*(6316-235x)= 37896 +169x - 58.75x².

B). If $ 5.75 is charged for a small bag of apples, then the quantity sold would be 6316+235 = 6551 small bags of apples so that the revenue would be 6551*$ 5.75 = $ 37668.25. Alternatively, on substituting x = -1 in the value of R arrived at in part A0 above, the revenue would be 37896 -169 - 58.75 = $ 37668.25.

C). Let the price be $ 6+0.25x when the sales are $ 30000. Then 30000 = 37896 +169x - 58.75x² or, 58.75x² -169x - 896 = 0. A graph of this function is attached. It may be observed that the graph crosses the X-Axis at x = -2.723 and x = 5.6. Hence, the sales would be $ 30000, when the price per small bag is $ 6.00-2.723*0.25 = $ 5.32 or $ 6+5.6*0.25 = $ 7.40. If we round off x to the nearest whole number, then these prices would be $ 6-3*0.25 = $ 5.25 and $ 6+6*0.25 = $ 7.50 respectively.

milcah answered 2 years ago

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