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Constrained Optimization: One Internal Binding Constraint Wetzel Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $300 and $600, respectively. Assume initially that Wetzel can sell all that is produced of either component. Part A requires two hours of assembly, and B requires five hours of assembly. The firm has 300 assembly hours per week. Required: 1. Express the objective of maximizing the total contribution margin subject to the assembly-hour constraint. Objective function: MaxZ=$300A+$600B Subject to: X A+B 2. Identify the optimal amount that should be produced of each machine part. If none of the components should be produced, enter " 0 " for your answer. Component A units Component B units Identify the total contribution margin associated with this mix. $ 3. What if market conditions are such that Wetzel can sell at most 75 units of Part A and 60 units of Part B? Express the objective function with its associated constraints for this case. 3. What if market conditions are such that Wetzel can sell at most 75 units of Part A and 60 units of Part B? Express the objective function with its associated constraints for this case. Objective function: MaxZ=$300A+$600B Assembly-hour constraint \begin{tabular}{l|l} & A+B \\ A & \\ B & \end{tabular} Demand constraint for Part B B Identify the optimal mix and its associated total contribution margin. Component A $ units Component B \$ units Total contribution \$ Feedback Check My Work 1. The objective function can be expressed mathematically by multiplying the unit contribution margin by the units to be produced for each product and then summing over all products. An internal constraint is a limiting factor found within the firm and is expressed as an inequality, where the amount of scarce resource used per unit of product is multiplied by the units to be produced for each product and summed. This is compared to the amount of the resource available