Assume that additional workers are hired for the bottleneck operation to expedite setups and materials handling. The cost of the additional workers is US $50,000 per year. As a result, the annual output of the bottleneck operation will increase by 500 units. The change in operating income attributable to the increase in workers is:
Answer(s): C
Operation 2 is the bottleneck because it is functioning at its capacity. The incremental annual throughput contribution revenues -- direct materials costs) from adding workers to Operation 2 is US $36,000 [500 units x $120 unit price -- $48 DPI per unit)]. Because the cost of the additional workers is US $50,000, the change in operating income is US $ 14,000). This information is relevant to a theory of constraints TOG) analysis. A manufacturer that can sell all of its output produces its sole product using three operations. Each unit sells for US $120, and direct materials costing US $48 per unit are added at the start of the first operation. Other variable costs are immaterial. The fallowing annual cost and capacity information is available concerning those operations:
Assume that C Company offers to perform the operation 2 function on 1,000 units at a unit price of US $40, excluding direct materials cast. Also assume that Y Company offers to perform the Operation 1 function an 1,000 units at a unit price of US $7, excluding direct materials cost.Which of these mutually exclusive offers is acceptable?
Answer(s): A
KG's offer should be accepted because its cast is US $40,000 1,000 units x $40), but the increase in throughput contribution is US $72,000 [1,000 units $120 unit price -- $48 E' 1 per unit)]. Hence, the relevant cost of QC's offer is less than the incremental throughput contribution. ms's offer effectively increases the capacity of the bottleneck operation. Y's offer should be rejected because, even though its US $7 unit price is less than the US $8 unit operating cost excluding direct materials) for Operation 1. it will result in the incurrence of additional casts with no increase in throughput contribution, given that Operation 2 is already producing at its 150,000-unit capacity.
Company J produces two components: A-1 and A-2. The unit throughput contribution margins for A-1 and A-2 are US $150 and US $300, respectively. Each component must proceed through two processes: Operation 1 and Operation 2. The capacity of Operation 1 is 180 machine hours, with A-1 and A-2 requiring 1 hour and 3 hours, respectively.Furthermore, Company J can sell only 45 units of A-1 and 100 units of A-2. However,Company J is considering expanding Operation 1's capacity by 90 machine hours at a cost of US $80 per hour. Assuming that Operation 2 has sufficient capacity to handle any additional output from Operation 1, how much should Company J produce?
A-1's throughput contribution margin per unit of the scarce resource the internal binding constraint) is US $150 $150 UCM - 1 machining hour). A-2's throughput contribution margin per unit of the scarce resource is U $100 $300 UCM - 3 machine hours).Consequently, Company J should produce as much A-1 as it can sell 45 units). If Company adds 90 machine hours to increase the capacity of Operation -I to 270 hours 180 + 90), it cannot produce additional units of A-1 because the external binding constraint has not been relaxed. However, it can produce additional units of A-2. Given that the UCM per machine hour of A-2 is U $100 and that the cost is US $80 per hour, adding capacity to Operation 1 is profitable. Thus, Company J should use 45 machine hours to produce 45 units of A-1. The remaining 225 machine hours 270 - 45) should be used to produce 75 units 225 - 3 hours) of A-2. The latter amount is within the external binding constraint. A company produces two products, and Y, which use material and labor as inputs. Fixed amounts of labor and material are available for production each month In addition. the demand for product Y each month is limited: product has no constraint an the number of units that can be sold. A graphical depiction of these production and demand constraints is presented in the opposite column.
The feasible solution region is bounded by the lines connecting points:
A model consisting of a system of functions may be used to optimize an objective function. If the functions in the model are all linear, the model is a linear programming model. Linear programming is a technique to determine optimal resource allocation. Several solution methods are available to solve linear programming problems. The graphical method, the easiest technique, is limited to simple problems. Here, the graph consists of three lines, each representing a production constraint. The lines connecting points , 4, 6, and 7 bound the feasible solution region. Product mikes of and Y that lie outside this boundary cannot be produced and/or sold because the demand constraint line ,4), the labor constraint line 4,6), and the material constraint line 6,7) are binding. A company produces two products, and Y, which use material and labor as inputs. Fixed amounts of labor and material are available for production each month In addition. the demand for product Y each month is limited: product has no constraint an the number of units that can be sold. A graphical depiction of these production and demand constraints is presented in the opposite column.
If a series of profit lines for and Y are drawn on the graph, the mix of G and Y that will result in the maximum profit can be determined from:
A profit line has negative slope because the profit from sales of one product increases as the profit from sales of the other product declines. Moving the profit line rightward while maintaining its slope) to the last paint in the feasible region determines the solution.
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