+89 2. A dressmaker has fixed monthly costs of e1,350. Her variable material costs per dress are e34, and she sells the finished product for e79 each.
(a) Find the total cost function, and the total revenue function.
(b) How many dresses have to be sown and sold per month for her to break even?
(c) Find the profit function, and determine the profit when 90 dresses are sown and sold per month.
(d) How many dresses have to be sown and sold per month to yield a monthly profit of e4,500?
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a) TC = 1350 + 34U
TR = 79U
b) Breakeven = 24.54 (25)
c) P= 55U - 1350
P= 3600
d)106.36 (107)
+118612 a is correct.
If you show your working for the others I will check it. They are too hard to do in my head. :)
+89 A dressmaker has fixed monthly costs of e1,350. Her variable material costs per dress are e34, and she sells the finished product for e79 each
(b) How many dresses have to be sown and sold per month for her to break even?
(c) Find the profit function, and determine the profit when 90 dresses are sown and sold per month.
(d) How many dresses have to be sown and sold per month to yield a monthly profit of e4,500?
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b) P= 79n - (1350 +34n)
P= 55n - 1350
P= 1350/55 = n
breakeven = 24.54 or 25
c) P= 55(90) - 1350 = 3600
d) 55n -1350= 4500
55n = 5850
n=5850/55
n= 106.36 (107)
+128707 (a) Find the total cost function, and the total revenue function.
(b) How many dresses have to be sown and sold per month for her to break even?
(c) Find the profit function, and determine the profit when 90 dresses are sown and sold per month.
(d) How many dresses have to be sown and sold per month to yield a monthly profit of e4,500?
(a) TC = 1350 + 34U
TR = 79U
(b) Breakeven
1350 + 34U = 79U
1350 = 45U
U = 30
(c) Profit = TR -TC
79(90) - [1350 + 34(90)] = 2700
(d)
4500 = 79U - [ 1350 + 34U]
4500 = 45U - 1350
5850 = 45U
U = 130
Here's a graph of the profit function with e break-even point and the points in (c) and (d) plotted :
https://www.desmos.com/calculator/johprfhcwy
