Q4. Hashtag Café sells three types of desserts: brownies, chocolate puddings and cheesecakes. Each brownie requires one ounce of sugar, three ounces of cream cheese and one ounce of chocolate. Each chocolate pudding requires two ounces of sugar and four ounces of chocolate. One ounce of sugar and 2 ounces of cream cheese are needed to make a cheesecake. The amounts of sugar, cream cheese and chocolate available are 430 ounces, 460 ounces and 420 ounces, respectively. The profit for each brownie, chocolate pudding and cheesecake are RM3, RM2 and RM5, respectively. Let x₁, x2 and x3 be the number of brownies, chocolate puddings and cheesecakes, respectively, the linear programming model and its associated optimal simplex tableau are given as Maximize z = 3x₁ + 2x₂ + 5x3 Subject to Basic X₂ X3 -Z x₁ + 2x₂ + x3 ≤ 430 (sugar) 3x₁ + 2x3 ≤ 460 (cream cheese) x₁ + 4x₂ S 420 (chocolate) X1, X₂, X3 20 x₁ -0.25 1.5 2 -4 X₂ 1 0 0 0 X3 0 1 0 0 0.5 0 -2 -1 Xs -0.25 0.5 1 -2 X₂₁₂₁ 0 0 1 0 Solution 100 230 20 -1350 (a) If the baker purchases additional amounts of 150 ounces of cream cheese and 110 ounces of chocolate, find the new optimum solution by using sensitivity analysis or post-optimal analysis. Comment on your answer. (b) Determine the feasibility range of the availability of cream cheese.