Problem 1
In the LOGO Production Expanded problem (with 10 products, done in Homework 2 — attachedl), we have modeled the constraint that each product can only be produced in at most one plant in class. Now consider the alternative scenario where there are no restrictions in the number of plants to use for each product, but instead, there is a $100,000 fixed cost for setting up making each product at each plant. For example, if Santa’s Grotto is only produced at Plant 1 but not Plant 2, a fixed cost of $100,000 is incurred; if it is produced at both Plant 1 and Plant 2 (regardless of actual quantities produced), a fixed cost of $200,000 is incurred; and if the product is not made at all (i.e., not sold), there are no fixed cost for this product.
Model this in your spreadsheet and solve for the optimal solution. Hint: this is related to the integer programming model.
Problem 2
Refer to the Advertising Budget Optimization problem (attached). Solve the problem with Excel Solver, and produce the sensitivity report. For the constraint on the advertising budget (currently $40,000):
Interpret the meaning of the Lagrangian multiplier.
Increase the advertising budget by $10. Resolve the problem – how does the optimal profit change? How does that compare to what the Lagrangian multiplier predicts?
Increase the advertising budget by $40,000. Resolve the problem – how does the optimal profit change? How does that compare to what the Lagrangian multiplier predicts?