Respuesta :
Answer:
a)C(x)=1500+35x
b)R(x)=60 x
c)P(x)=25x-1500
d)The number of lessons that must be held for the studio to break even ia 60
e)The studio will make 550 if 82 lessons are held
Step-by-step explanation:
Monthly cost that include rent, utilities, insurance, and advertising = $1500
The studio charges $60 for each private lesson but has a variable cost for each lesson of $35 to pay the instructor.
a)Write a linear cost function representing the cost to the studio C(x) to hold x private lessons for a given month
Fixed monthly cost = $1500
Variable cost of trainer for each lesson = $35
Variable cost of trainer for x lessons = 35x
So, C(x)=1500+35x
b)Write a linear revenue function representing the cost to the revenue R(x) to hold x private lessons for a given month
Charge for 1 lesson = 60
Charge for x lessons = 60 x
So, R(x)=60 x
c)Write a linear profit function representing the cost to the profit P(x) to hold x private lessons for a given month
Profit = Revenue - Cost
P(x)=R(x)-C(x)
P(x)=60x-1500-35x
P(x)=25x-1500
d)Determine the number of lessons that must be held for the studio to break even
R(x)=C(x)
60x=1500+35x
25x=1500
x=60
So, the number of lessons that must be held for the studio to break even ia 60
e) If 82 lessons are held during a month how much money will the studio make or lose
P(x)=25x-1500
P(82)=25(82)-1500
P(82)=550
So, The studio will make 550 if 82 lessons are held
1)Profit function P(p)=25p-1500
2) For the break-even number of lessons to be held is 60 lessons.
3)Profit, when 82 sessions are held is $550.
The fixed monthly cost of the dance studio= $1500
The variable cost of the trainer for each lesson = $35
So, Variable cost of trainer for 'p' lessons = 35a
So, Total cost =1500+35p
Charge for 1 private lesson = 60
Charge for 'p' lessons = 60p
So, Revenue =60p
We know that, Profit = Revenue - Cost
So, Profit =60p-(1500+35p)
Profit=25p-1500
What is the break-even point?
The break-even point is the point at which total cost and total revenue are equal.
For break-even
Cost = Revenue
1500+35p = 60p
p =60
So, for the break-even number of lessons to be held = 60 lessons
Profit when 82 sessions are held
Profit = 25p-1500
Profit = 25*82-1500
Profit = $550
Therefore, 1)Profit function P(p)=25p-1500
2) For the break-even number of lessons to be held is 60 lessons.
3)Profit, when 82 sessions are held is $550.
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