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.

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