s. University Ceramics manufactures plates, mugs, and steins that include the ca
ID: 359097 • Letter: S
Question
s. University Ceramics manufactures plates, mugs, and steins that include the campus name and logo for sale in campus bookstores. The time required for each item to through two state for production (molding and finishing) and the material required (clay) and the corresponding amount of each resource available in the upcoming production period. Molding (minutes) 4 Finishing (Minutes) 8 Clay (ounces) Profit per unit $ 3.10 $ 4.75 $ 4.00 14 12 7200 A line ar programming model has been formulated to determine the production levels that would maximize profit. The sensitivity report form that model is given below. Variable Cells Final Reduced Objective ValueCost Coefficient Increase Decrease Cell $G$11 Name Plates Mus Steins 300 3.1 2.233333333 0.366666667 4.75 0.458333333 0 -0.458333333 400 I$11 0.65 1.375 Constraints Final Shadow Constraint Allowable Allowable R.H. Side Increase Decrease Value Price Cell $GS14 Molding (minutes) Amount Used 2400 0.216666667 SG 15 Finishin Minutes) Amount Used 7200.27916667 $6S16 Clay (ounces) Amount Used Name 2400 200 600 200 3000 2400 300 2400 a. How many plates, mugs, and steins should be produced? Suppose the profit per plate decreases from $3.10 to $2.80, would the optimal production quantities change? Explain how you know. b.Explanation / Answer
a) Plates = 300, Mugs = 0, Steins = 400
b) Allowable decrease for profit per plate is 0.36667.
Decrease in profit per plate = 3.1-2.8 = 0.3
Therefore, this is within allowable range of decrease and hence. optimal production quantities do not change.
c) Total change as percentage of allowable range in profit per stein and plate = 0.30/0.65 + 0.25/0.36667 = 114%
This is more than 100%, therefore optimal production quantities would change.
d) Shadow price of Finishing constraint is 0.279167
Allowable increase in Finshing time is 2400. Therefore, shadow price is valid for 600 minutes increase, and applicable change in profit per minute is 0.279167
Total increase in profit for 600 minutes = 600*0.279167 = $ 167.5
Total cost of 600 minutes is $ 120. Therefore, increase in profit is enough to offset the additional cost.
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