Solve the linear programming problem.
-The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2
Man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the
Company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?
A) 18 VIP and 6 SST
B) 12 VIP and 12 SST
C) 14 VIP and 10 SST
D) 16 VIP and 8 SST

Question

Quizplus · Accepted Answer

To maximize profit, we set up the following linear programming problem with the constraints given: Let x be the number of VIP rings and y be the number of SST rings produced daily. The constraints are:1. $3x + 2y \leq 60$ (man-hours constraint)2. $x + y \leq 24$ (production capacity constraint)3. $x, y \geq 0$ (non-negativity constraint)The objective function to maximize is the profit: $P = 40x + 35y$.Graphing these constraints, the feasible region is determined. The vertices of this region are where the maximum or minimum of the objective function can occur. By evaluating the profit at each vertex of the feasible region, we find that the combination of 12 VIP rings and 12 SST rings (option B) provides the maximum profit within the given constraints.

Solve the Linear Programming Problem