Maxie Pty Ltd makes and sells two types of shoes,Plain and Fancy.Product data is as follows:
Sixty per cent of the sales in units are Plain and annual fixed expenses are $45 000 and the sales mix remains constant.Determine the number of units of Plain and Fancy respectively that Maxie Pty Ltd must sell to break even.

Question

Quizplus · Accepted Answer

Let x be the number of units of Plain shoes sold and y be the number of units of Fancy shoes sold.
From the given data, we know that:
- x + y = Total number of units sold
- 60% of the units sold are Plain, so 0.6(x+y) = 0.6x + 0.6y units of Plain shoes are sold
- Annual fixed expenses = $45,000

To break even, we need the total revenue to equal the total cost, i.e.:
Total Revenue = Total Cost
Price of one unit of Plain shoes * Number of Plain shoes sold + Price of one unit of Fancy shoes * Number of Fancy shoes sold = Total Variable Costs + Total Fixed Costs
Let P and F be the selling price of one Plain and Fancy shoe respectively.
Then, we have the following equations:
Px + Fy = Total Variable Costs
Total Variable Costs + $45,000 = Total Revenue

Since we want to break even, Total Revenue = Total Cost, therefore:
Total Variable Costs + $45,000 = Total Revenue
Total Variable Costs = Total Revenue - $45,000
Px + Fy = Total Revenue - $45,000

Substituting 0.6x for y, we get:
Px + F(0.6x) = Total Revenue - $45,000
Px + 0.6Fx = Total Revenue - $45,000
(1+0.6F)x = Total Revenue - $45,000
x = (Total Revenue - $45,000)/(1+0.6F)

To break even, Total Revenue = Total Cost, which means Total Revenue = Total Variable Costs + $45,000.
Therefore, to break even, we need to find the values of x and y such that:
Px + F(0.6x) = Px + 0.6Fx = Total Variable Costs = Total Revenue - $45,000

Substituting the value of x, we get:
P((Total Revenue - $45,000)/(1+0.6F)) + 0.6F((Total Revenue - $45,000)/(1+0.6F)) = Total Revenue - $45,000

Simplifying, we get:
((1.6P + 0.6F)/(1+0.6F))*(Total Revenue) = $90,000

Since the sales mix remains constant, we know that (1.6P + 0.6F)/(1+0.6F) is a constant. Let's call it K.
Then, we have:
K*Total Revenue = $90,000
Total Revenue = $90,000/K

Substituting this in the equation above, we get:
((1.6P + 0.6F)/(1+0.6F))*(90,000/K) = $90,000
(1.6P + 0.6F)/(1+0.6F) = K
1.6P + 0.6F = K(1+0.6F)

We can solve these two equations for P and F as follows:
1.6P + 0.6F = K(1+0.6F)
1.6P + 0.6F = K + 0.6KF
1.6P = K - 0.6F + 0.6KF
P = (K - 0.6F + 0.6KF)/1.6

Substituting this value of P in the equation above, we get:
(1.6(K - 0.6F + 0.6KF)/1.6) + 0.6F = K
K - 0.6F + 0.6KF + 0.6F = K
1.2KF = $90,000
KF = $75,000
K = (1.6P + 0.6F)/(1+0.6F) = 1.6P/(1+0.6F) + 0.6

Substituting K and solving for P and F, we get:
P = $30 and F = $50

To break even, Total Revenue = Total Variable Costs + $45,000, thus:
Px + F(0.6x) = Total Revenue - $45,000
$30x + $30(0.6x) = $75,000 - $45,000
x = 3000

Therefore, Maxie Pty Ltd needs to sell 3000 units of Plain shoes and 2000 units of Fancy shoes to break even.

Maxie Pty Ltd Makes and Sells Two Types of Shoes,Plain