You plan to sell cupcakes to raise funds.a bakery charges you a 15 pesos for the 100 cupcakes.After the first 100 cupcakes you purchase up to 150 cupcakes,the bakery lower the price to 13.50 pesos pe cupcakes.After you purchase 150 cupcakes the price will decrease 10.00 Pesos per cupcake.Write a function that models this situation
Answers
Answer:
P(x) = (15)x when x < 100 or x = 100
P(x) = 15(100) + (x - 100)13.5 when 100 < x < 150 or x = 150
p(x) = 15(100) + 13.5(50) + (x - 150)10 when 150 < x
Step-by-step explanation:
Let P(x) denote the price function
x denote the quantity of cupcakes
Then
Price function for the given situation in the question is given as piece wise function
P(x) = (15)x when x < 100 or x = 100
P(x) = 15(100) + (x - 100)13.5 when 100 < x < 150 or x = 150
p(x) = 15(100) + 13.5(50) + (x - 150)10 when 150 < x
Given : a bakery charges them P15.00 for the first 100 cupcakes .after the first 100 cupcakes they purchase up to 150 cupcakes the bakery reduce the price to P13.50 per cupcake.after they purchased 150 cupckaes,the price lower to P10.00 per cupcakes.
To Find : Write a function that models this situation
Solution:
x = number of Cup cakes
f(x) = Charges
P15.00 for the first 100 cupcakes
f(x) = 15x 0 < x ≤ 100
after the first 100 cupcakes they purchase up to 150 cupcakes the bakery reduce the price to P13.50 per cupcake.
f(x) = 15*100 + (x - 100)13.5 = 13.5x + 150
f(x) = 13.5x + 150 100 < x ≤ 150
for 150 cups = 2175
After they purchased 150 cupckaes, the price lower to P10.00 per cupcakes.
f(x) = 2175 + (x - 150) 10 = 10x + 2025
f(x) = 10x + 2025 150 < x
Piece wise function :
15x 0 < x ≤ 100
f(x) 13.5x + 150 100 < x ≤ 150
10x + 2025 150 < x
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