Each day, a factorys total expenses are equal to a fixed daily

Question

Each day, a factory’s total expenses are equal to a fixed daily expense plus a variable expense that is directly proportional to the number of units of product produced by the factory during that day. If the factory’s total expenses for a day in which it produces 3,000 units are $5,500, and the total expenses for a day in which it produces 7,000 units are $8,200, what is the factory’s fixed daily expense?

A. 3400
B. 3425
C. 3450
D. 3475
E. 3500

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Purnank · Answer

Assume F as fixed cost, V as a variable  cost per unit  and n as number of units.
Variable price is directly proportional to number of units, Therefore for n=3000 variable cost will be "3000V" and for n=7000 "7000V"

as per given conditions in question lets form two equations for total expenses of factory for production of 3000 and 7000 units.

Equation 1: 5500 = F (fixed cost) + 3000V (variable cost)
Equation 2: 8200 = F (fixed cost) + 7000V (variable cost)

Solving both equations we will get the value for V = 27/40 and  F=3475 (The required answer)

Hence Option D.

Nidzo · Answer

Let the fixed daily expense =  a 
Let the variable expense =  b

The factory’s total expenses for a day in which it produces 3,000 units are $5,500:   a + 3000b = 5500

The total expenses for a day in which it produces 7,000 units are $8,200:   a + 7000b = 8200

Subtracting equation 1 from equation 2:   4000b = 2700

b = \frac{27}{40}

Plugging this back into  a + 3000b = 5500 :

a + 3000(\frac{27}{40}) = 5500

a = 5500 - 2025

a = 3475

ANSWER D

BrushMyQuant · Answer

Each day, a factory’s total expenses are equal to a fixed daily expense plus a variable expense that is directly proportional to the number of units of product produced by the factory during that day.

Total Expense = Fixed + Variable * Number of units produced

If the factory’s total expenses for a day in which it produces 3,000 units are $5,500

Total Expense = Fixed + Variable * 3000 = 5500 ...(1)

T he total expenses for a day in which it produces 7,000 units are $8,200

Total Expense = Fixed + Variable * 7000 = 8200 ...(2)

What is the factory’s fixed daily expense?

(1) * 7 - (2) * 3

=> 7 * (Fixed + Variable * 3000) - 3 * (Fixed + Variable * 7000) = 7 * 5500 - 3 * 8200
=> 7 * Fixed - 3 * Fixed + 21000 * Variable - 21000 * Variable = 100 * (385 - 246)
=> 4 * Fixed = 100 * 139
=> Fixed = 25 * 139 = 3475

So,  Answer will be D 
Hope it helps!

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https://www.youtube.com/watch?v=dRxzi_x3ZwY

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