Fixed costs of production, math problem
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Fixed costs of production, math problem

[From: ] [author: ] [Date: 11-11-08] [Hit: ]
8. A company has fixed costs of €2,500, and the total costs of producing 200 units is €3,300.a.......
Hey guys, im studying for my math test tomorrow and I am trying to solve this question;



8. A company has fixed costs of €2,500, and the total costs of producing 200 units is €3,300.
a. Assuming linearity, write down the cost-output equation.
b. If each item produced sells for €5.25, find the break-even point.
c. How many units should be produced and sold so that a profit of €200 results

Only the answers are given, no explanation. So could anyone help me out?

btw this are the end answers;

8. a) yc=4x+2,500 b) 200 units c) 2,160 units



Thanks alot

-
a)
The total costs consist of the fixed costs plus the per-unit costs of production. If the total costs are €3,300 and the fixed costs are €2,500, then the per-unit costs of producing 200 units are (€3,300 - €2,500) = €800. Assuming linearity, if it costs €800 to produce 200 units, then it costs €800/200 = €4 per unit. So if x units are produced, the total costs will be (in €) 2500 + 4x

b)
The break-even point is where the revenue equals the total costs. If a unit sells for €5.25, then x units sell for €5.25x. If this equals the total costs for producing those x units, then

5.25x = 2500 + 4x
1.25x = 2500
x = 2000

You must have a typo there.


c)
Let x denote the number of units that must be sold to obtain a profit of €200. Profit is total revenue minus total costs. From part (a) we obtained an expression for the total costs of producing x units. As with part (b), the total revenue is the unit cost (€5.25 here) times the number of units sold. So x satisfies

5.25x - (4x + 2500) = 200
1.25x = 2700
x = 2160 units

-
a) Cost = Variable cost + Fixed cost
y = ax + b = ax + 2500
When x = 200, cost = 3300. Therefore,
3300 = 200a + 2500
a = 4
Therefore, y = 4x + 2500

If selling price is 5.25, the revenue is R = 5.25x.
Break even is x for R = y.
5.25x = 4x + 2500
1.25x = 2500
x = 2500/1.25 = 2000 is the break even point.

Profit = Revenue - Cost
P = R - y
P = 5.25x - 4x - 2500 = 1.25x - 2500

P =200 gives
200 = 1.25x - 2500
x = 2700/1.25 = 2160
1
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