Linear Programming

NewCrest is looking to invest at most $500,000. The investment can be divided among three options. The return on each option depends on the economic outlook, which is shown in Table 1. For example, if the economic outlook is bright, investing $1 in option I will generate a gain of $3, and investing $1 in option 11 will result in a loss of $5. Table 1: Return 31' dollar invested in the different options Return E dollar invested in option Economic outlook I II III Bright 3 -5 7 Gloomy -2 6 -3 \"Defme x1 = investment in option I, x2 = investment in option I], and x3 = investment in option III. The objective is to Maximize min {3x1 5x; + 7x3, 2x1 + 6x; 3x3]\". The objective function is not linear. Please search online \"tricks to maximize the min of objective Jnctions\" or 'ansformations into linear programs\". How to convert the above nonlinear objective function to a linear objective function