$($a$)$ A consumer purchases a flat iron to straighten her hair for Rs$.7,500$ from a salon at which she gets her haircut. If the salon's markup is $40\%$ and the wholeseller's markup is $15\%,$ both based on their selling prices, for what price does the manufacturer sell the product to the wholeseller $?$

$($b$)$ If the unit variable cost for each flat iron are Rs$\mathrm{.}2,000$ and the manufacturer has fixed costs totalling Rs$.10,000,000,$ how many flat irons must this manufacturer sell to break$-$even $?$ How many must it sell to realize a profit of Rs$.40,000,000?$

$4$