Problem 1 Solve: The Logo Production Problem

Problem 1solve The Logo Production Problem The Base Version With Only

Solve the LOGO Production problem (the base version with only two products—see attached Excel file) using Excel Solver and produce the Sensitivity Report. Using the sensitivity report without resolving the problem, predict whether the optimal solution changes under various scenarios: (1) the Selling Price for Santa’s Grotto increases from $55 to $80, (2) the Selling Price for Advent Calendar decreases from $35 to $22, (3) the Material Cost for Santa’s Grotto increases from $15 to $45, (4) the Material Cost for Advent Calendar decreases from $8 to $20. Additionally, for each case where the optimal solution does not change, predict the new optimal profit without resolving the problem and show your workings.

Paper For Above instruction

The production problem involving two products—Santa’s Grotto and the Advent Calendar—requires optimizing profit based on various constraints regarding resources, costs, and prices. Utilizing Excel Solver allows determining the optimal production quantities that maximize profit under the current parameters. Once the Solver finds this optimal solution, generating a Sensitivity Report provides insights into the stability of this solution when parameters change.

The core of the problem is to maximize profit by deciding the number of units of each product to produce, given constraints such as resource availability, production costs, and selling prices. Variables typically include quantities of Santa’s Grotto and Advent Calendars. The objective function is calculated as the sum of profits per product, considering selling price minus material cost, multiplied by production quantities. Constraints encompass resource limitations such as machine hours, material availability, and demand limits.

Using the Sensitivity Report, which includes the shadow prices and allowable increases/decreases, allows prediction of how changes in key parameters affect the optimal solution without re-solving unless necessary. For example, if the allowable increase in the selling price of Santa’s Grotto from $55 exceeds the change to $80, and the shadow price is high, the optimal production plan is likely to shift favorably, increasing profit. Conversely, if the decrease in material costs for Advent Calendar from $8 to $20 stays within the allowable decrease, then the optimal solution generally remains unchanged, with profit increasing by the difference in material costs for the same production quantities.

Specifically, predictions based on the sensitivity report can include:

• If the allowable increase in Santa’s Grotto price includes the new price of $80, then the optimal solution remains, but profit increases accordingly, calculable as the change in price times the quantity produced, as long as this change does not exceed the allowable range.
• If the decrease in cost for Santa’s Grotto stays within its allowable decrease, the same applies: the solution remains, and the profit increases proportionally with the reduction in material costs.
• Similarly, if the selling price of Advent Calendar drops from $35 to $22 within the permissible allowable decrease, the optimal solution remains producing the same quantities, but the profit decreases proportionally to the drop in unit profit.
• Any change exceeding the allowable ranges would necessitate re-solving, but within them, the solution remains optimal, and the profit can be updated by recalculating the profit formula with the new parameters.

For each parameter change, detailed calculations involve multiplying the change in unit profit or cost by the quantity of production that responds to the change, often inferred from the shadow prices and allowable ranges. These predictions help decision-makers understand potential profit impacts and sensitivities without recalculating the entire model repeatedly.

References

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