Maximum Production

Chefland has $7$ days in a week. Chef is very conscious about his work done during the week. There are two ways he can spend his energy during the week. The first way is to do $x$ units of work every day and the second way is to do $y$ ($\gt x$) units of work for the first $d$ ($\lt 7$) days and to do $z$ ($\lt x$) units of work thereafter since he will get tired of working more in the initial fe