Question

In: Operations Management

A manufacturing company is selling two products, rods and reels, each at $65 per unit. Rods...

A manufacturing company is selling two products, rods and reels, each at $65 per unit. Rods have a variable cost of $30. Reels have a variable cost of $25. Fixed cost for the company is $22,000.

a. If the sales mix is 1:1, (1 rod to 1 reel) what is the breakeven in units of rods and reels?

b. If the sales mix is 1:1, (1 rod to 1 reel) what is the break-even point in dollars of sales?

c. If the sales mix changes to 1:4, (1 rod to 4 reels) what is the break-even point in units of rods and reels?

d. If the sales mix changes to 1:4, (1 rod to 4 reels) what is the break-even point in dollars of sales?

Solutions

Expert Solution

Let the no. of rods be x and no. of reels be y.

As seen from data, x = y.

We will first find the breakeven equation and then substitute value of x.

Selling price of each item = $65

Fixed cost = FC = $22000

Variable cost for rod = VCd = $30

Variable cost for reel = $25

At breakeven, profit = 0

Profit = Total Revenue - (Fixed costs + Variable costs)

0 = Selling price of each item * (No. of rods + No. of reels) - (22,000 + Variable cost for rod * No. of rods + Variable cost for reel * No. of reels)

0 = 65 * (x + y) - (22000 + 30 * x + 25 * y)

35x + 40y = 22000................................................................Equation 1

x = y

75x = 22000

x = y = 293.33

Brekeven in terms of dollars = Total Revenue = 65 * (293.33 + 293.33) = $38,133.33

Hence,

a. If the sales mix is 1:1, (1 rod to 1 reel), the breakeven in units of rods and reels is 293.33 units of each

b. If the sales mix is 1:1, (1 rod to 1 reel), the break-even point in dollars of sales $38,133.33

For part c & D,

Sales mix = 1 : 4

4x = y

As per equation 1 above,

35x + 40y = 22000

35x + 40(4x) = 22000

x = 112.82

y = 4x = 451.28

Brekeven in terms of dollars = Total Revenue = 65 * (112.82 + 451.28) = $36,666.5‬

c. If the sales mix changes to 1:4, (1 rod to 4 reels), the break-even point in 112.82 units of rods and 451.28 units of reels.

d. If the sales mix changes to 1:4, (1 rod to 4 reels), the break-even point in dollars of sales = $36,666.5‬

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keosha answered 2 months ago
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