Question

A group of middle school students wants to raise money to help build a new school track. They decided to sell donuts before school. Demand is 275 donuts when the donuts are given away free, and the demand drops to 175 donuts when the price is 25 cents per donut. However, the middle school administration is prepared to supply only 150 donuts free of charge but will supply 200 donuts when the price is 50 cents per donut. Assume that the demand and supply functions are both linear functions. What price should the students charge per donut so that there is neither a surplus nor a shortage of donuts

Answer 1

25 cent/donuts

Step-by-step explanation:

Demand function have these two points (275, 0), (175, 25)

Demand function equation:

y - 25 =
`(25 - 0)/(175-275)` (x-175)

-100y + 2500 = (x - 175)

-4y + 100 = x - 175

x + 4y = 100 + 175

x + 4y = 275....................equ 1

Similarly Supply function have these point (150,0), (200, 50)

Supply function equation:

y - 50 =
`(50 - 0)/(200-150)`(x- 200)

50y - 2500 = x - 200

y - 50 = x - 200

x - y = 200 - 150

x - y = 150

By equation 1 & 2

x + 4y = 275

x - y = 150 ==> x = 150+y

So from equ 1 => x + 4y = 275

=> 150+y+4y = 275

=> 150+5y = 275

=> 5y = 275 - 150

=> 5y = 125

=> y = 25

So, the price that the students should charge per donut so that there is neither a surplus nor a shortage of donuts is 25 cent/donuts