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[($14(54,000) + $11(40,000) – ($2.00(54,000) + $1.25(40,000)) – $6.00*(0.5(54,000) + 0.3(40,000))] * (1.00 - 0.28) = $578,880To determine which constraints are binding we need to look at the slack or surplus values indicated in the LINGO model solution shows in Appendix of the report. A binding constraint is one where the slack or surplus is 0. The LINGO output shows constraints 4 and 6 have 0 slack orsurplus values, and therefore, we can conclude that the maximum production of footballs and maximum hours of machine utilization are the binding constraints. RecommendationsGiven ABCD’s current productive capacity and constraints, the recommended productionmix would be to manufacture 56,000 basketballs and 40,000 footballs, as previously stated. However, if the company is searching for a strategy to improve profitability, there are a few courses of action they could take; increase hours of machine utilization, produce different quantities of their products, or change the retail price of their products. As a consultant, my suggestion would be to manufacture 60,000basketballs and 40,000footballs. This mix maximizes the firm’s productive capabilities according the facilities constraints and yields higher profits. We can use the shadow prices as well as the ranges of allowable increases and decreases to explain. Referring again to Appendix A, the LINGO output shows a shadow price of zero for the basketball production constraint while the sensitivity
5INDIVIDUAL CASE STUDY – ABCD,LTD.analysis shows an allowable increase of 2000, bringing machine hours to 42,000.Thus, increasing the number of basketballs to 60,000 allows ABCD’s other constraints to remain with their range of feasibility. The calculations below show the effect of this change on after-tax profit.0.5B + 0.3F = 42,0000B + 0.3F = 42,000F = 140,0000.5B + 0F = 42,000B = 84,000Production Costs:60,000 X $2 = $120,00040,000 X $1.25 = $50,000$6 x 42,000 = $252,000Total Cost = ($120,000 + $50,000 + $252,000) = $422,000Sales Revenue:$14 x 60,000 = $840,000$11 x 40,000 = $440,000Total Revenue = $1,280,000Profit = Revenue – Costs - TaxesNet Profit = $1,280,000 – $422,000Net Profit = $858,000 (0.72)Net Profit = $617,760Therefore, the organizations net profit would increase from $578,880 to $617,760if 60,000 basketballs and 40,000 footballs are manufactured. In Appendix C, we see the LINGO output that confirms this course of action. When we change the R.H. side of constraint 6 to