Question

# The Commerce Students’ Society orders cloth patches embossed with the business school’s crest. The patches have...

The Commerce Students’ Society orders cloth patches embossed with the business school’s crest. The patches have Velcro to attach them over the pocket of a jacket. The patches come in a box containing 75 units. The manufacturer has stipulated that patches must be ordered in boxes. The cost of each patch to the society is \$2.21. The society intends to sell each patch for \$5.37. Student volunteers selling the patches are to be paid a commission of \$0.47 for each patch sold. The school admits 325 students each year. The society hopes to sell each student a patch and consequently has placed an order for the minimum number of boxes required to sell at least 325 patches. How many patches must be sold for the society to break even?

It is to be noted that Commerce Students’ Society has ordered the minimum number of boxes required to sell at least 325 patches.

Number of patches required = 325 batches

Patches per box = 75

Number of minimum box required = 325 / 75 = 4.33

Since the society cannot place order for partial box of patches, it will have to order 5 boxes of patches.

Total Cost for a box (75 patches) = 75* \$2.21 = \$165.75

Selling price per batch = \$5.37

Variable cost per patch (commission) = \$0.47

Contribution per patch = \$5.37 - \$0.47 = \$4.90

Break-even point = Total Cost/ Contribution per unit

= \$165.75 / \$4.90

= 33.83

Hence Society needs to sell at least 34 patches to recover its entire cost.

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