Report writing Example
DS-523
Galaxy Industries is an emerging toy manufacturing company that produces two “space Age” water guns that are marketed nationwide, primarily to discount toy stores. Although many parents object to the potentially violent implications of these products, the products have proven very popular and are in such demand that Galaxy has had no problem selling all the items it manufactures.
The two models, the Space Ray and the Zapper, are produced in lots of one dozen each and are made exclusively from a plastic compound. Two of the limiting resources are the 1000 pounds of the special plastic compound and the 40 hours of production time that are available each week.
Galaxy’s marketing department is more concerned with building a strong customer demand base for the fledgling company’s products than with meeting high production quotas. Two of its recommendations, which Galaxy’s management has already accepted, are to limit total weekly production to at most 700 dozen units and to prevent weekly production of space Rays from exceeding that of Zappers by more than 350 dozen. The following table summarizes the per dozen resource requirements and profit values (calculated by subtracting variable production costs from their wholesale selling prices).
Products / Profit per dozen / Plastic (lb.) per dozen / Production Time (min.) per dozenSpace Ray / $8 / 2 / 3
Zapper / $5 / 1 / 4
Galaxy’s production manager argued that since the $8 profit per dozen Space Rays exceeds the $5 profit per dozen Zappers by 60%, the company would maximize its profit by producing as many Space Ray as possible, while remaining within the marketing guide lines. That is, if the resources were sufficient, Space Ray production should exceed Zapper production by 350 dozen, with the combined total production not exceeding 700 dozen. Using a trial and error approach he suggested a production schedule of 450 dozen Space Rays and 100 dozen Zappers weekly, giving Galaxy a profit of $4100 per week or 52($4100) = $213,200 per year.
Although this was considered a good profit, upper management began to question whether a different production schedule might increase company profit. Exactly what production combination of Space Rays and Zappers are possible for Galaxy Industries? And, of these possible production values, which maximizes the objective function?
Write a report that compares the results of the recommended policy to those of the current policy at Galaxy Industries. Your report should summarize the results and detail the distribution of resources as well as sensitivity analysis that might be of interest to the management. Include a copy of your linear programming model and graphical solution in the appendix to your report.
MEMORANDUM
To:Hal Barnes, Production Manager, Galaxy Industries
From:your Name
Date:01/18/2019
Re:Optimal production quantities for Space Rays and Zappers
Galaxy Industries wishes to determine production levels for its Space Ray and Zapper water gun, which will maximize the company’s weekly profit. It is our understanding that production of these products occurs in batches of one dozen each.
Physical production limitations include the amount of plastic (1000 pounds) and available production time (40 hours) to the company on a weekly basis. In addition, the company wishes to adhere to marketing recommendations that limit total production to 700 dozen units weekly and restrict weekly production of Space Rays to a maximum of 350 dozen more than the number of Zappers produced. Current weekly production levels of 450 dozen Space Ray and 100 dozen Zappers result in a $4100 weekly profit for Galaxy.
We have had the opportunity to determine the plastic and production time requirements for these products and to analyze Galaxy’s situation. By assuming profit and production requirements are fixed and constant, we were able to solve this as a linear programming model using Excel.
Analysis and Recommendation: Based on the results of our model, we recommend that Galaxy change its production levels to the following:
Space Rays / 320 dozenZappers / 360
Weekly Profit / $4360
The current proposed policies are compared in table 1
Table 1.Current vs. Proposed Policies-Galaxy Industries
Current Policy (Weekly basis)Production
(doz.) / Plastic
(lb.) / Production time
(hr.) / Profit
($)
Space Rays
/ 450 / 900 / 22.50 / 3600Zappers / 100 / 100 / 6.67 / 500
Total / 550 / 1000 / 29.17 / 4100
Unused / 0 / 10.83
Proposed Policy (Weekly basis)
Production
(doz.) / Plastic
(lb.) / Production time
(hr.) / Profit
($)
Space Rays
/ 320 / 640 / 16.00 / 2560Zappers / 360 / 360 / 24.00 / 1800
Total / 680 / 1000 / 40.00 / 4360
Unused / 0 / 0
As this table indicates, both policies produce less than the limit of 700 dozen suggested by the marketing department. The proposed policy has a more balanced production of Space Rays and Zappers than the present production policy. Under the current policy, weekly production of Space Rays exceeds that of Zappers by the maximum limit of 320 dozen. Under the proposed plan, production of Zappers actually exceeds that of Space Rays by 40 dozen per week.
The $4360 weekly profit corresponding to recommended production schedule represent a 6.34% (or $260) increase in weekly profit, of 13525 annually. This amount could be used to increase marketing of the current products, fund production of the new Big Squirt model, or lease more efficient machines to improve product profit contributions.
The next part is sensitivity analysis.
Although this model is based on profit projection of $8 per dozen Space Ray units and $5 per dozen Zapper units, our analysis reveals that our recommendation would remain unchanged unless the Space Ray profit is higher than $10.00 or lower than $3.75 (a 25% underestimation or a 95% overestimation), or the Zapper profit is higher than $10.67 or lower than $4.00 (a 113% underestimation or a 20% overestimation). We are confident that our profit projections fall well within this margin of error.
If the Galaxy has the opportunity to purchase additional plastic from its vendor, our analysis shows that it will prove profitable to purchase up to 100 additional pounds of plastic, as long as the cost does not exceed $3.40 per pound over its normal cost. If the additional 100 pounds of plastic are purchased, giving a total of 100 pounds of plastic, our recommendation is to produce 400 dozen Space Rays and 300 dozen Zappers.
If more than 100 pounds of plastic were available, it would be profitable to purchase up to an additional 125 pounds of plastic (for a total of 1225 pounds) as long as the cost of these additional 125 pounds does not exceed $3.00 per pound. If a total of 1225 pounds of plastic were available, we recommend a production schedule of 525 dozen Space Rays and 175 dozen Zappers.
There is insufficient production time to use more than 1225 pound of plastic while still adhering to marketing department recommendation that Space Ray production not exceed Zapper production by more than 350 dozen.
In lieu of purchasing plastic, if Galaxy considers scheduling overtime, we recommend that scheduling up to 1 and 2/3 hours of overtime weekly be profitable if total overtime cost do not exceed $24 over the normal hourly wage arte. Using this overtime, the company should produce 300 dozen Space Rays and 400 Zappers weekly.
Production Recommendations with additional Resources
Additional Resources
/ Space Rays (doz.) / Zapper(doz.) / Weekly profit
($)
150 pounds of Plastic / 400 / 300 / 4700
225 pounds of plastic / 525 / 175 / 5075
1 2/3 overtime hours / 300 / 400 / 4400
These recommendations are based on changes in only one resource –Plastic or overtime.
Appendix
The Mathematical Model
Decision Variables:
X1 = number of dozen Space Rays produced Weekly
X2 = number of dozen Zappers produced weekly
Objective Function
Maximize 8X1 + 5X2
Constraints:
Plastic
Production Time
Total Production Limit
Balanced Product Mix
Computer Out put
LINEAR PROGRAMMING PROBLEM
MAX 8X1+5X2
S.T.
1) 2X1+1X2<1000
2) 3X1+4X2<2400
3) 1X1+1X2<700
4) 1X1-1X2<350
OPTIMAL SOLUTION
Objective Function Value = 4360.000
Variable Value Reduced Costs
------
X1 320.000 0.000
X2 360.000 0.000
Constraint Slack/Surplus Dual Prices
------
1 0.000 3.400
2 0.000 0.400
3 20.000 0.000
4 390.000 0.000
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
------
X1 3.750 8.000 10.000
X2 4.000 5.000 10.667
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
------
1 600.000 1000.000 1100.000
2 1750.000 2400.000 2500.000
3 680.000 700.000 No Upper Limit
4 -40.000 350.000 No Upper Limit
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