Answer Happy

a 7.M.3 I'm a chemist trying to produce four chemicals: Astinium, Bioctrin, Carnadine, and Dimerthorp. When I run Process 1, I produce one gram of Astinium, one gram of Bioctrin, 5 grams of Carna- dine, and 3 grams of Dimerthorp. When I run process 2, I produce 3 grams of Astinium, one 3 gram of Bioctrin, one gram of Dimerthorp, and I consume one gram of Carnadine. My target is to produce 100 grams of all four chemicals. I know this is not precisely possible, but I want to get as close as possible (with a least squares error measurement). How many times should I run process 1 and process 2 (answers need not be whole numbers)?
7.W.2 Return to the setting of exercise 7.M.3. It turns out that Astinium is far more reactive than the other chemicals, so getting the amount of Astinium close to the target is relatively more important. 23 A ---|| 100 100 If b = is the desired amount of each chemical, and 6 = is the amount we actually 100 100 D produce, then we desire to minimize the weighted sum of squares error 4(100 – A)2 + (100 – B)2 + (100 – C)2 + (100 – D)?. a) Define an inner product on R4 so that the weighted sum of squares error above is equal to 1|6 — @112 b) Write down the normal equation for this optimization problem (using the setup from 7.M.3) which determines the best amount of each process to run. c) Solve this normal equation.