A manager wants to decide production amounts of 4 products A, B, C, D in order to maximize profit. The profits are $29, $32. $72 and $54 per unit of A, B, C and D produced, respectively. Materials E and Fand labor hours are limited resources. The problem can be modelled as follows: Decision Variables: A = Amount of product A B = Amount of product B C = Amount of product D = Amount of productD Max Z=29A + 328 + 72C + 540 in $ of profit) Subject to 3A + 4 + 4C + 3D S 4700 (material E) 2A + 2B + 4C + 3D S 4500 (material F) A+ B + 3C + 2D S 2500 (labor hours) A B C D 20 (nonnegativity! By using the software output below, answer the following questions Variable Cells Name Cost Cell $A$3 A $B$3 B $C$3 C SD$3D Final Reduced Objective Allowable Allowable Value Coefficient Increase Decrease 0 -1 1 LE30 380 40 1.666666667 0 72 8 15.30 1060 0 10 5 Constraints Final Shadow Constraint Allowable Cell Name Value Price R.H. Side Increase $B$12 Material E 4700 2 4700 2800 $B$14 Material 3940 0 4500 $B$16 Labour hours 2500 24 Allowable Decrease 950 580 1325 a. How many units of products A. B, C, D should be produced in order to maximize profits, and what is the optimum profit value? b. In what dollar range can the profit per unit of product Dvary without changing the optimal solution i.e. the optimum A B, C, D values) c. Suppose that the profit per unit of product Dis decreased to $50, how this change wil affect the optimum objective function value d. A suggestion is made to increase the availability of materials E and Fat the additional cost of $1/hr. Is this advisable? Assume that 5 units of product C have been produced by mistake. What is the resulting effect on profit (state whether it is a decrease/ increase in profit and the amount)