A craftsman can sell 10 jewelry sets for $500 each. He knows
for each additional set he makes, the price of each set will decrease by $25. Hoy
many jewelry sets should he make if he wants to maximize his earnings?
jewelry sets

The craftsman should make 5 additional jewelry sets to maximize his earnings

The cost of 10 jewelry sets is given as: $500 per set

For every increment in the number of jewelry sets, the selling price decreases by $25

Let x represents the number of jewelry sets.

The cost function is:

Expand

Differentiate

Set to 0

Add 50x to both sides

Divide both sides by 50

Hence, he should make 5 additional jewelry sets to maximize his earnings

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15

Step-by-step explanation:

Given

Craftsman sell 10 Jewelry set for $500 each

For each additional set he will decrease the price by $ 25

Suppose he sells n set over 10 set

Earning

Earning

differentiate to get the maximum value

Equate to get maximum value

Thus must sell 5 extra set to maximize its earnings.

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