Develop and solve a linear programming model to maximize contribution to profit. Let \\( R_{\\mathrm{i}}= \\) the number of barrels of input \\( \\mathrm{i} \\) to use to produce Regular, \\( i=1,2,3 \\) \\( S_{i}= \\) the number of barrels of input \\( i \\) to use to produce Super, \\( \\mathrm{i}=1,2,3 \\) If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300 ) \\[ \\mathrm{R} 1, \\mathrm{R} 2, \\mathrm{R} 3, \\mathrm{~S} 1, \\mathrm{~S} 2, \\mathrm{~S} 3 \\geq 0 \\] What is the optimal contribution to profit? Maximum Profit \\( =\\$ \\) by making barrels of Regular and barrels of Super