Solve the following linear programming problem graphically. What is the optimal solution and what is the maximum possible value for the objective function?
Maximize 12X + 10Y
Subject to: 4X + 3Y ≤ 480
2X + 3Y ≤ 360
all variables ≥ 0
Also Formulate this as a linear programming problem 20 Points
A plastic parts supplier produces two types of plastic parts used for electronics. Type 1 requires 30 minutes of labor and 45 minutes of machine time. Type 2 requires 60 minutes of machine hours and 75 minutes of labor. There are 600 hours available per week of labor and 800 machine hours available. The demand for custom molds and plastic parts are identical. Type 1 has a profit margin of $25 a unit and Type 2 have a profit margin of $45 a unit. The plastic parts supplier must choose the quantity of Product A and Product B to produce which maximizes profit.