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At the doctor's advice, you are supposed to consume 100% of the Recommended Daily Allowance (RDA) of protein, carbohydrate and calcium, 80% of fat, and 75% of salt. You select 5 food items for the day and you need to figure out how many servings of each you need to eat to stay with your diet. The nutritional content of the foods you selected, per serving, is as follows: % of RDA per serving Food protein carbohydrate fat salt calcium ---- ------- ------------ --- ---- ------- A 0 15 10 10 15 B 30 20 20 10 20 C 20 25 10 20 15 D 30 15 30 10 20 E 10 15 0 20 5 1. Set up the problem as a linear systemAx=b. Try to arrange the matrix A so that no pivoting will be necessary, if you can. 2. Use Matlab to find the LU factorization of A: [L,U]=lu(A) . (>> diary onto record your work in file "diary", specifyformat shortfor readability). Is L really lower triangular ? If not, use[L,U,P] = lu(A)to find the necessary permutation matrix P, then find the LU factorization of the matrix PA. Is L lower triangular now ? 3. Use Matlab to solve your system Ax=b. Round the values to integers. Is this a feasible diet ? Why ? What can you do to get a proper diet for the day ? 4. Solve the system with forward and backward substitutions, in Matlab, using L and U appropriately. Does the solution agree with the one found in 3. ? Submit, all in a single text file "lab3.txt" (can use Matlab notation for matrices): a. Your matrix A and vector b from 1. -------------------------------------------- b. The L and U from 2, and if for A or for PA. -------------------------------------------- c. Answers to 3, unrounded and rounded. -------------------------------------------- d. What systems you solved, in symbols (like: Ly = b, ....), and the solution, from 4. --------------------------------------------