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At ABC Co., sales revenue is $170,000 when it spends $5000 on advertising. Sales revenue is $254,000 when $12,000 is spent on advertising. a) Find a linear function for y = amount of sales revenue as a function of x = amount spent on advertising. b) Find revenue if $10,000 is spent on advertising. c) Find the amount that should be spent on advertising to achieve $200,000 in revenue.

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Answer:

Given y = cost

X = units

Y = a+bx

a = fixed cost

b = dy/dx = Vc/unit

bx =Vc

Using high and low method of cost segregation; the total of this function can be identified

Cost(y) Units

High. 12,000. 254,000

Low. (5,000). (170,000)

dy: 7,000. dx:

84,000

Given ; TC = y = a+bx

Where y = amount spent on adverts

a = fixed cost elements

x = Sales revenue

b = variable and per unit

b = dy/dx =Vc/units

b = dy/dx

Given dy = 7,000

dx= 84,000

b = dy/dx = 7,000/84,000 =0.083

Checking for constancy of fixed asset.

At x = 254,000

y = a + 0.083(254,000)

y = a + 21,082

But Y = 12,000

12,000 = a + 21,082

a = - 9082

At x = 170,000

y = a + 0.083(170,000)

5,000 = a + 14,110

a = - 9110

a = - 9110 = - 9083 ( approximately)

Since a = fixed cost = approximately constant,

Y = a + 0.083x

Where a = - 9110

A. Y = -9110 + 0.083x

B. Find Revenue I.e x

When y = 10,000

Y = -9110 + 0.083x

10,000 = -9110 + 0.083x

10,000 + 9110= 0.083x

19,110 = 0.083x

x = 19,110/0.083

= $230, 240.96

C. The amount that should be spent on advertising to achieve $200,000 in revenue

Given ; y = a + bx

y = -9110 + 0.083x

y = -9110 + 0.083 (200,000)

y = -9110 + 16,600

y = $7,490

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