Pro Peds, a local athletic shoe manufacturer, makes a training shoe at a cost of

Question

Pro Peds, a local athletic shoe manufacturer, makes a training shoe at a cost of $22 per pair. This cost includes raw materials and labor only. A check of previous factory runs indicates that 10% of the training shoes will be defective and must be sold to Odd Tops, Inc., as irregulars for $32 per pair. If Pro Peds produces 1,000 pairs of the training shoes and desires for the total selling price from the sale of these shoes to include a markup of 100% on the cost of the entire 1,000 pairs of shoes, find the markup rate based on cost:

Explanation / Answer

cost price of a pair of shoes = $22
total no. of pairs of shoes = 1,000
total cost price = 22 x 1,00
= $22,000
no of defective pairs of shoes = 10% of 1,000
= 100
the selling price of a pair of defective shoes = $32
total = 32 x 100
= $32,00

desired markup = 100% on c.p
= $22,000

therefore desired profit = $22,000
profit = S.P-C.P
22,000 = S.P -22,000
S.P = $44,000

let x be the selling price of a non defective pair
then,

S.P = 32,00 + 900x
44,000 = 3200 + 900x
x = (44,000 - 3200)/900
=$45.33

Mark up rate = (S.P - C.P)/ C.P

Markup rate for defective pair = (32-22)/22
= 0.454545

Markup rate for a non-defective pair = (45.33 - 22)/22
= 1.06045

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