Electronic equipment manufacturer Dynamo electric makes several types of surge p
ID: 3018911 • Letter: E
Question
Electronic equipment manufacturer Dynamo electric makes several types of surge protectors. Their base model surge protector has monthly fixed costs of $1275. This particular model retails for $14 each and costs $6.50 per unit to manufacture
a) write the function for dynamos monthly costs
c(x)= ?
b) Write function for dynamos monthly revenue
R(x)=?
c) Write function for dynamos monthly profit
P(x)=?
d) Find the number of this type of surge protectors thtat dynamo must produce each month to break even
2) If in a monopoly market the demand for a product is p=170 -0.10x and the revenue function is R=px, whre x is the number of units sold , wht price will maximize revenue?
3) If a company has a total cost of C(x)= 45,000+45x+.3x2 and total revenue given by R(x)= 635x-0.7x2, find the break even point
Explanation / Answer
1)
a) Let x be the no. of model produced
Total cost = Fixed Cost + Variable Cost
As per question,
Fixed Cost = $1275
Variable cost for x products produced = 6.5*x = 6.5x
=> Total Cost = c(x) = 1275 + 6.5x
b) Monthly Revenue
R(x) = 14.x
$14 is retail price
c) Profit
P(x)= R(x) -c(x) = 14x - (1275 + 6.5x) = 14x -6.5x - 1275 = 7.5x - 1275
d) Break even
P(x)=0
=> 7.5x -1275 = 0
=> 7.5x = 1275 => x = 1275/7.5 = 170 units
On producing 170 units, break even will occur
2) R(x) =px
p=170 -0.10x
R(x) = (170 - 0.1x) *x= 170x - 0.1x2
For maximum revenue , first derivative should be zero
=> d(R(x))/dx = d(170x -0.1x2)/dx= 170 - 0.2x= 0
=> 0.2x = 170
=> x =170/0.2
=> x = 850
For 850 units, revenue will be maximum
Price = 170 - 0.10(850) = 170 - 85 =$ 85
This price will maximize revenue
3) For Break even
C(x)= R(x)
=> 45000 + 45x + 0.3x2= 635x - 0.7x2
=> 45000 + 1x2 +45x - 635x = 0
=> x2 - 590x +45000=0
=> x2 - 500x -90x +45000= 0
on factorising
=> x(x - 500) - 90 ( x - 500) =0
=> x= 90 or x = 500
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