Baker’s Pantry (BP) is well-known for its large sourdough loaves. It makes two versions: the San Francisco and the Sacramento. They are almost the same size and weight but use different combinations of Danish and Swedish wheat flour, wild yeast from Germany and specialist French sea salt, all of which are in limited supply in Padstow, at the moment. The table below sets out the requirements for each loaf (in grams), together with current daily supply of each ingredient. The profit contribution of each San Francisco loaf is £4, while that of a Sacramento loaf is £5.

 

a) Shelley has come across a Managing Accounting textbook which she used on her Business Management course many years previously. It talks about a decision-making technique known as ‘limiting factor/constrained resource analysis’, but she has only a vague memory of how it is applied. Explain to her whether it would be a suitable technique in this decision problem. (5 marks)

b) Formulate this as a linear programming problem, where the aim is to determine the optimal combination of sourdough loaves to produce each day to maximise the company’s profit contribution. (7 marks)

c) Do not graph: Identify the binding constraints using the Excel Sensitivity Report, below, and use this information to solve the problem algebraically. Indicate the number of loaves of each type to produce each day and the maximum achievable daily profit contribution. (10 marks)

d) Using information on the shadow price of each constraint in the Excel Sensitivity Report for the problem, below, calculate how much additional profit BP would gain from a 10% increase in the daily supply of (i) Danish Flour and (ii) Swedish Flour. (6 marks)

e) By how much would the supply of Sea Salt have to fall before it becomes a binding constraint? Explain your reasoning. (3 marks)

f) Using the Excel Sensitivity Report, identify the range of profit contribution for each loaf over which the optimal solution identified in (c) remains valid. Interpret this for Shelley.

 

San Francisco Sacramento Total Supply Danish Flour 225 300 9,000 Swedish Flour 400 200 12,000 Wild Yeast 30 40 1,800 Sea Salt 10 10 400