Jasmine owns a jewelry store and marks up the price from the distributor to earn a profit. she buys a necklace for $100, a pair of earrings for $130, and a ring for $160 . she wants to earn at least $40 on each of the items but does not want to mark up any price by more than $80. a. what is the range of percents that jasmine can markup each item so that it fits into her criteria b. suppose jasmine wants to markup all 3 items using the same percent but also maximize her profit. what percent should she use c. using the percent from part b, find each marked up price d. using the results from part c, find her total profit

A. Jasmine buys a necklace for $100 and wants to earn at least $40 on it but does not want to mark price by more than $80. In this case $40 is 40% {(40:100)·100%} and $80 is 80% {(80:100)·100%}. Then the range of the percent that Jasmine can mark up necklace is [40%,80%].

She also buys a pair of earrings for $130 and wants to earn at least $40 on it but does not want to mark price by more than $80. In this case $40 is nearly 31% {(40:130)·100%} and $80 is 62% {(80:130)·100%}. Then the range of the percent that Jasmine can mark up necklace is [31%,62%].

At last, she buys a ring for $160 and wants to earn at least $40 on it but does not want to mark price by more than $80. In this case $40 is nearly 25% {(40:160)·100%} and $80 is 50% {(80:160)·100%}. Then the range of the percent that Jasmine can mark up necklace is [25%,80%].

B. She should use the maximal number from the left end and the minimum number from the right end, so she should use percent from the range [40%, 50%]. If she wants to maximize her profit, she should select 50%.

C. If she mark up any price by 50%, then the price of a necklace will become $150 {(150%:100%)·100}, the price of a pair of earrings will become $195 {(150%:100%)·130} and the price of a ring will be $240 {(150%:100%)·160}.

D. She pays in total $100+$130+$160=$390. After selling these jewerlies she gets $150+$195+$240=$585. The difference is $585-$390=$195 - her total profit.