In a month, I can sell 420 of my unlicensed Warriors T-shirts at a price of...

In a month, I can sell 420 of my unlicensed Warriors T-shirts at a price of $12. At $18, I sell 180. The T-shirts cost me $8 each, and I bribe the local law enforcement $300 per month to use a corner near a BART station to sell my shirts.

1. Assume price-demand is linear

a. Find the slope of the price-demand function.

b. Find the vertical-intercept of the price-demand function.

c. Write a function to predict demand (in a month) given any price.

d. Predict the demand at a price of $10.

e. What price fetches a demand of 800 shirts?

2. Assume cost is linear.

a. Write a function to predict cost (in a month) given any price.

b. Predict the cost at a price of $10.

Expert Solution

Price-demand is linear
slope of the price-demand function ((420-180)/(12-18))	(40)
*Vertical-intercept of the price-demand function ((12-(-40)+420) or ((18-(-40)+180)*	900
Function to predict demand (in a month) given any price (Where P means Price and Q means Quantity sold)	Q = 900 - 40P
*Predict the demand at a price of $10 (900-(4010))**	500
What price fetches a demand of 800 shirts
Q = 900 - 40P
800 = 900 - 40P
800 + 40P = 900
40P = 900 - 800
40P = 100
P = 100 / 40
P = 100 / 40 = $2.50
What price fetches a demand of 800 shirts	$ 2.50

cost is linear
Fixed cost per Month	$ 300
Variable cost per T-shirt	$ 8
Function to predict cost (in a month) given any price (where Y means cost and X means Quantity Sold)	Y = 300 + 8X
Predict the cost at a price of $10
When the price is $ 10 then 500 T-shirts sold.
*Predict the cost at a price of $10 (300+8(500))**	$ 4,300

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