Question

1. 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:

Type of sandwhich	Decision Variables	Min. No of units sold	Preparation time per unit (minutes)	Profit per unit ($)
Tuna Mayo	T	200	0.40	0.42
Ham and Cheese	H	200	0.50	0.44
Cheese and Salad	C	200	0.48	0.35
Spicy Vegetable	S	200	0.55	0.46

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.

Refer to above Excel output, 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 would happen to the total daily profit?

		The total daily profit will decrease by $0.0067.
		Nothing.
		The total daily profit will increase by $1.34.
		The total daily profit will decrease by $1.34.
		The total daily profit will increase by $0.0067.

How many of each type of sandwich should ALS produce each evening in order to maximize profit and what will this profit be?

		An optimal profit of $790 is achieved by producing 200 units of T; 200 units of H; 200 units of C & 200 units of S.
		An optimal profit of $790 is achieved by producing 200 units of T; 400 units of H; 1000 units of C & 400 units of S.
		An optimal profit of $790 is achieved by producing 200 units of T; 400 units of H; 400 units of C & 1000 units of S.
		An optimal profit of $790 is achieved by producing 400 units of T; 400 units of H; 400 units of C & 400 units of S.
		An optimal profit of $790 is achieved by producing 400 units of T; 200 units of H; 1000 units of C & 400 units of S.

Answer 1

1)

If you change the constraint for hamburger from 200 to 0 the profit will come tp 791.34

The total daily profit will increase by $1.34.

Option C

2)

As you can see in solver sheet

An optimal profit of $790 is achieved by producing 400 units of T; 200 units of H; 1000 units of C & 400 units of S.

Option E