You and your friend are playing a computer game on a server together. You need at least $10000$

more points in order to get the things you need for your next quest, so today you$$re doing some

grinding.

You can get $500$ points from playing the minigame, which takes you $4$ minutes. Your friend is

better at the minigame and can get $750$ points in the $4$ minutes. Each player can only play the

minigame once today. Either or both of you can collect stars in the forest obtaining $130$ points per

minute. You can also travel to the river and fish obtaining $300$ points per minute, but it takes you $3$

minutes to travel there and back. Your friend cannot obtain points at the river because they do not

have fishing as a skill. Assume players spend an integer number of minutes at the river and at the

forest.

You and your friend want to figure out how to each spend time on these tasks to minimize the

total number of player$-$minutes spent between the two of you in order to obtain at least $10000$ points.

Formulate this problem as an integer program.