Jack and Diane were saving money to go to a rock n roll concert. They need at least $750 in order to go if you count their gas, hotel, food, concert tickets, and souvenir money. Jack plays gigs at the local Tastee Freez and Diane car hops. Jack earns $50 per night that he plays, and Diane earns $25 each night she works. The number of nights Diane is scheduled to work is no more than four times the number of nights Jack is scheduled to play. Diane will work at least 10 times before the concert. Write a set of constraints to model the problem, with x representing the number of nights Jack worked and y representing the number of nights Diane worked.

Answer:[tex]\left\{\begin{array}{l}y\le 4x\\ \\x\ge 10\\ \\50x+25y\ge 750\end{array}\right.[/tex]Step-by-step explanation:Let x represents the number of nights Jack worked and y represents the number of nights Diane worked.1. The number of nights Diane is scheduled to work is no more than four times the number of nights Jack is scheduled to play. Then[tex]y\le 4x[/tex]2. Diane will work at least 10 times before the concert. Then[tex]x\ge 10[/tex]3. Jack earns $50 per night that he plays, then he earned $50x in x nights. Diane earns $25 each night she works, then she earns $25y in y nigths. They need at least $750, so[tex]50x+25y\ge 750[/tex]4. We get the following set of constraints to model the problem:[tex]\left\{\begin{array}{l}y\le 4x\\ \\x\ge 10\\ \\50x+25y\ge 750\end{array}\right.[/tex]