varibalbe cells inal value reduced cost objective coefficient allowable increase
ID: 3196965 • Letter: V
Question
varibalbe cells inal value reduced cost objective coefficient allowable increase allowable decrease cell name X2 X3 1000 1650 1350 0.6 0.55 0.7 1.00E+30 0.016666667 0.05 0.0125 0.83333333 0.15 0 Contraints final value shadow price contraint R.H. side allowable increase allowable decrease cell name contraint 1 contraint 2 contraint 3 1920 4000 1000 0.75 0.25 0.0125 1920 4000 1000 330 675 2200 270 550 1000 3. Answer the following questions by using the sensitivity analysis results (that is, the ranging results) from Question 2. Do NOT solve the problem again by using any computer software or website (a) If the profit from a ham and cheese sandwich increases from $0.60 to $0.75, will the optimal number the three kinds of sandwiches made change? Will the total profit change? If they change, what will be the new optimal solution and the new total profit? (b) If the profit from a grilled vegetables sandwich increases from $0.55 to S0.70, will the optimal number of the three kinds of sandwiches made change? Will the total profit change? (c) The company has an opportunity to acquire some extra minutes of sandwich making. What is the maximum price the company should pay for each minute of additional sandwich making time, and how many additional minutes of sandwich making should they acquire at that price?Explanation / Answer
3a) If the profit increase from 0.6 to 0.75 the optimal number of sandwiches made will not change since the maximum ham and cheese sanwich possible is 1000, since profit is increasing the number of sandwiches should increase but since the maximum possible constraint is already met hence, it cannot increase. The profit will change according to the change in profit per sandwich:
old total profit = 0.6*1000 +1650*0.55 + 1350*0.7 = 600+907.5+945 = 2452.5
new profit = 0.75*1000 + 907.5 + 945 = 2602.5
b) if profit from grilled veg sandwich increases the optimal number of sandwiches will not change since even with less profit iotimal number of sandwiches for grilled veg is high, and now the profit for chicken salad and grilled veg is same hence the current optimal value will be the same.
profit will change according to the new profit values:
old profit as calculate above = 2452.5
new profit = 600 + 0.7*1650 + 945 = 2700
c) minutes available is constraint 1
current value = 1920, shadow price = 0.75.
shadow price represents the profit gained per unit addition of available time of sandwich making.
Hence the maximum price they should pay should be 0.75 per unit time acquired.
Also, the maximum time they should acquire is 330, since the allowable increase for constraint 1 is 330.
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