Quantitative Analysis of Business Coursework Example | Topics and Well Written Essays - 2000 words

Quantitative Analysis of Business - Coursework Example Determine the equations for each of the three constraints that are plotted on the attached â€Å"graph 1†, showing all work necessary to arrive at the equations.  Determine the equations for each of the three constraints that are plotted on the attached â€Å"graph 1†, showing all work necessary to arrive at the equations.  Identify each constraint as a minimum or maximum constraint.   The objective function is Z= 30X+72Y+90Subject to   7.5X + 7.5Y ≠¤ 30 (equation for Nutrient C)    6X + 12Y       ≠¤ 72 15X + 6Y ≠¤ 90          X ≠¥ 0, Y ≠¥ 0 Since the feasible region is below the constraints the constraints are minimum constraints. Determine the total contribution to profit, if the company produces a combination of cases of brand X and brand Y that lies on the purple objective function (profit line) as it is plotted on the attached â€Å"graph 1†.If the company chooses to produce a combination of brand X and Y as given in graph then the different combinations would be (0, 8), (1, 6.6), (2, 5.4), (3, 4), (4, 2.6), (5, 1.3), (6, 0). The contribution to profit at various combinations can be obtained using the objective function where profit= 30X+72Y+90 and substituting the value of X and Y for each set in this function we get profit for each combination.When the company produces 8 units of Brand Y and no Brand X the profit function is maximized (666). But this combination is outside the feasible region. So, the combination that gives maximum profit (468) to the producer within the optimal region is 3 units of X and 4 units of Y. The Total Contribution of Profit: The total contribution to profit which can be obtained by producing 3 units of brand X and 4 units of brand Y is 468 which is obtained by putting the values of X and Y in the profit