Answer:
The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).
Step-by-step explanation:
This is a linear programming problem.
The objective function is profit R, which has to be maximized.
![R=40V+35S](https://tex.z-dn.net/?f=R%3D40V%2B35S)
being V: number of VIP rings produced, and S: number of SST rings produced.
The restrictions are
- Amount of rings (less or equal than 24 a day):
![V+S\leq24](https://tex.z-dn.net/?f=V%2BS%5Cleq24)
- Amount of man-hours (up to 60 man-hours per day):
![3V+2S\leq60](https://tex.z-dn.net/?f=3V%2B2S%5Cleq60)
- The number of rings of each type is a positive integer:
![V, \;S\geq 0](https://tex.z-dn.net/?f=V%2C%20%5C%3BS%5Cgeq%200)
This restrictions can be graphed and then limit the feasible region. The graph is attached.
We get 3 points, in which 2 of the restrictions are saturated. In one of these three points lies the combination of V and S that maximizes profit.
The points and the values for the profit function in that point are:
Point 1: V=0 and S=24.
![R=40V+35S=40\cdot 0+35\cdot 24=0+840\\\\R=840](https://tex.z-dn.net/?f=R%3D40V%2B35S%3D40%5Ccdot%200%2B35%5Ccdot%2024%3D0%2B840%5C%5C%5C%5CR%3D840)
Point 2: V=12 and S=12
![R=40V+35S=40\cdot 12+35\cdot 12=480+420\\\\R=900](https://tex.z-dn.net/?f=R%3D40V%2B35S%3D40%5Ccdot%2012%2B35%5Ccdot%2012%3D480%2B420%5C%5C%5C%5CR%3D900)
Point 3: V=20 and S=0
![R=40V+35S=40\cdot 20+35\cdot 0=800+0\\\\R=800](https://tex.z-dn.net/?f=R%3D40V%2B35S%3D40%5Ccdot%2020%2B35%5Ccdot%200%3D800%2B0%5C%5C%5C%5CR%3D800)
The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).