The sandwich company, Alamo Lone Star (ALS) prepares sandwiches for sale in vending machines in a large number of locations in an urban area. The four types of sandwich that are now provided are those that have been found to sell well. The following information is available on each type:

The most popular sandwich is the cheese and salad so ALS ensure that at least half of all sandwiches supplied are cheese and salad. All four types of sandwich are prepared each evening and then distributed to the vending machines the next morning. Sandwich preparation is carried out by five part-time workers. Four of these workers each work 3.5 hours each evening and one works for only two hours. KLS has 50 identical sandwich vending machines each with a capacity of 40 units.
The manager of ALS needs to know how many of each type of sandwich they should produce each evening in order to maximize profit subject to unit profit figures and constraints mentioned above. This problem was formulated as a linear programming model and then solved using Excel Solver. The Excel Solver output is provided in the appendix. Using the Solver output and where necessary the information given above, answer the following questions (include with your answers brief explanations). In each part of the question you must assume that any changes considered in any earlier part of the question have not been implemented.
Please note that to keep the model as simple as possible, it was assumed that ALS can sell all sandwiches they produced.

a) How much preparation time in total is available each evening for ALS? Please provide your answer in both hours and minutes.
b) In terms of the four decision variables, write down the constraint for preparation time. Pay special attention to units!
c) What is the maximum capacity in total for sandwiches in vending machines? (i.e. How many sandwiches can be put in total to the ALS’s
vending machines?).
d) How many of each type of sandwich should ALS produce each evening in order to maximize profit and what will this profit be?
e) ALS is considering some price changes. If ALS were to increase the unit price of spicy vegetable sandwich so that profit per unit becomes $0.53, would this have any effect on the optimal daily production schedule? Explain how you got your answer. If the optimal daily production is unchanged, what would be the total daily profit? Show your calculations. 

f) ALS is now considering making simultaneous (multiple) changes. The unit price of cheese and salad sandwich were to be increased so that the new profit per unit becomes $0.38. Also, the unit price of spicy vegetable sandwich were to be increased so that the new profit per unit becomes $0.53. Explain whether these multiple changes would have any effect on the daily optimal production schedule and any effect on the total daily profit? 

g) Janet, one of the four workers who work 3.5 hours each evening, wishes to reduce her time to 3 hours. Explain how this would affect the preparation time and explain whether this change is allowed. What effect will this change have on the total daily profit, if any? Show your calculations.
h) ALS is now worried about losing half an hour of preparation time. Joe, the person who currently works only two hours each evening, is aware of this and offered to do an extra hour if Janet reduces her time to 3 hours. What will the total preparation time available to ALS be if both Janet and Joe make the changes mentioned above? What will be the total profit per day be with these new hours? Explain and show your calculations.

i) One of ALS’s vending machines breaks down.
i. If this machine cannot be repaired or replaced for three days, how much profit will ALS lose over three days? (4 points)
ii. ALS has been offered to rent a vending machine with a capacity of 60 units for $18 a day. Should ALS accept this offer? 

j) ALS has concerns about their supplier of ham and has decided to switch to a new supplier. Because of this switch, for just one day they will not be able to supply any ham and cheese sandwiches. What do you think would happen to the total daily profit? Show your calculations. 

 

Transcribed Image Text:

Decision Minimum no. Preparation time Profit per Type of sandwich variables Tuna mayonnaise of units sold per unit (minutes) unit ($) 200 0.40 0.42 Ham and cheese H 200 0.50 0.44 Cheese and salad 200 0.48 0.35 Spicy vegetable 200 0.55 0.46 Decision Minimum no. Preparation time Profit per Type of sandwich variables Tuna mayonnaise of units sold per unit (minutes) unit ($) 200 0.40 0.42 Ham and cheese H 200 0.50 0.44 Cheese and salad 200 0.48 0.35 Spicy vegetable 200 0.55 0.46

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a There are total 5 workers out of which 4 work for 35 hours and 1 worker who work f... View the full answer