A Consultant Dietician provides diet and nutritional advice to clients. A client's diet requires that all the food s/he eats come from one of the four "basic food groups" (chocolate cake, ice cream, soda, and cheese-cake). At present, the following four food types are available: brownies, chocolate ice cream (in scoops), cola (in bottles), and pineapple cheese-cake (in pieces). Each food type has a price per unit. Each day, s/he must intake a minimum required amount of calories and minimum required amounts of chocolate (gm.), sugar (gm.) and fat (gm.).
You are working as a business analyst for the Consultant Dietician. The linear programming model has been formulated and analysed. Your task is to examine the answer and sensitivity reports, interpret the values based on the questions 'a' to 'g' and write a report to the Consultant Dietician that can be used to satisfy the client's daily nutritional requirements at a minimum cost.
The output (answer report and sensitivity report), from Excel's Solver, are given in Table 3 and Table 4 respectively (see page 4). Using the output given on page 4, Answer all questions and comment your results.
a) Write the mathematical expression of the Linear Programming problem for the objective function and state the constraints with the minimum required daily intake.
b) What is the optimal solution, in terms of the client's daily intake, that satisfies the daily nutritional requirements at a minimum cost? Be specific and give your answer in the context of the problem?
c) Calculate the value of the objective function using the information provided in Table 3 and Table 4? Show your calculations and give your answer in the context of the problem?
d) Are all resources fully utilised? Identify the resource(s), if any, that was not fully utilised or surplus. Be specific and give your explanation in the context of the problem.
e) For any resource identified in part (d), what amount of this resource initially set as a minimum requirement? What amount of this resource has slack/surplus? Show your calculations and give your answer in the context of the problem.
f) What is the impact on the optimal solution and the value of the objective function if the unit price for Pineapple cheese-cake increases to £1.50? Give your answer in the context of the problem.
g) What is a shadow price? The shadow price for daily calorie intake is 0. Explain the significance of this value in the context of the problem.
h) Write a short business report (of 600 words) to advice the Consultant Dietician that satisfies the client's daily nutritional requirement at a minimum cost. You will discuss the decision variables, optimal solution, value of objective function, shadow prices, the slack/surplus variables and evaluate the impact of changes on the combination and amounts of food types that provide the required nutrition at the least total cost.