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Difficulty: HardProfit, Loss, and Markup

A boutique jewelry designer crafts customized gold necklaces. The total cost to produce each necklace is the sum of a fixed material cost of $800\$800 and a variable design cost. To determine the list price, the designer marks up the total production cost by 60%60\%. During a seasonal promotion, the designer offers a 25%25\% discount off the list price. If the designer earns a net profit of $360\$360 on each necklace sold during the promotion, what is the variable design cost, in dollars, per necklace?

Answer: 1000 dollars

Answer

The variable design cost per necklace is $1,000.
The total production cost per necklace is C=800+LC = 800 + L. Marking up by 60%60\% yields a list price of 1.60C1.60C. A 25%25\% discount reduces the price to 0.75×1.60C=1.20C0.75 \times 1.60C = 1.20C. The net profit per necklace is 1.20C−C=0.20C1.20C - C = 0.20C. Given that the net profit is $360\$360, we set 0.20C=3600.20C = 360, which gives C=1,800C = 1,800. Subtracting the fixed material cost of $800\$800 yields the variable design cost of $1,000\$1,000.

Step-by-Step Solution

1
Define total production cost in terms of variable cost
C=800+LC = 800 + L, where CC is total production cost and LL is variable design cost
Total cost is the sum of fixed material cost and variable design cost.
2
Determine the selling price after markup and discount
Selling Price S=0.75×(1.60C)=1.20CS = 0.75 \times (1.60 C) = 1.20 C
A 60%60\% markup increases total cost by a factor of 1.601.60, and a 25%25\% discount reduces that marked price to 75%75\% (0.750.75).
3
Formulate the profit equation and solve for total production cost CC
Profit =S−C=1.20C−C=0.20C=360  ⟹  C=1,800= S - C = 1.20 C - C = 0.20 C = 360 \implies C = 1,800
Net profit is the selling price minus the total production cost.
4
Calculate variable design cost LL
L=1,800−800=1,000L = 1,800 - 800 = 1,000
Subtract fixed material cost from total production cost.

Key Concept

Profit, Loss, and Markup with Successive Percentage Adjustments
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Topics

Profit, Loss, and Markup

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