Caf Store has just designed a new drip coffee maker focused on better extraction of coffee solubles (CS) into the product coffee. Their coffee maker is designed to hold 1 liter of water. The dry coffee placed in the filter contains 99% coffee grounds and 1% coffee solubles. Caf Store has analyzed their product coffee (S3) and found it contains 0.4% CS and 99.6% water and the waste product (S4) contains 80% CG, 19.6% water and 0.4% CS. (All percentages are on a volume basis.) The company forgot to measure the volume of the various streams. They have heard engineers are excellent at solving material balances and have hired you to determine the volumes for S2, S3 and S4. A material balance is simply a mathematical statement that all of the water (for example) going into the process has come out again. (This assumes a steady state with no chemical reactions.) The following water balance is shown as an example: water in S1 = water in S3 + water in S4 1 S1 = 1 liter = 0.996 S3 + 0.196 S4 1) Write the system of linear equations that describes the material balances of water, CS, and CG. (This linear system has 3 equations and 3 unknowns.) 2) Put the equations in matrix form. 3) Solve the system of equations using Python, then solve them in Excel to check your answer.