Mathematical expression of linear programming problem, Programming Languages

Assignment Help:

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.


Related Discussions:- Mathematical expression of linear programming problem

Create a fortran program for represent a convex polygon, In analytical geom...

In analytical geometry, a convex polygon can be represented by the Cartesian coordinates of its vertices, x and y. Assume such data of a polygon are stored in a file called "vertic

Draw data structure and analyse on xml, The scenario As an XML expert y...

The scenario As an XML expert you are required to model a system for an online furniture shop. After an interview with the shop manager you have the following information: T

Program to output a triangle wave, 1.) Write a flowchart and program to do ...

1.) Write a flowchart and program to do the following: A pressure sensor in a cooling system measures the pressure of the refrigerant and is connected to Port -1 of the 8051. If th

C programming, Write an interactive C program which prompts the user with t...

Write an interactive C program which prompts the user with the following options on the opening menu: 1) Student information 2) Theory counselling batch-scheduling

Describe informally how to draw a pda diagram, Suppose L is a context-free ...

Suppose L is a context-free language and L' is regular. Show that L∩ L' is a context- free language. Specifically, if you're given a PDA diagram of L and a DFA diagram for L' , des

Write an implementation for the prime machine, You should use the BToolkit ...

You should use the BToolkit to produce the answers to the questions below. Where applicable, please use the machine names and identifier names suggested in the question to help me

Prims algorithm for minimum spanning tree, Implement the Prim's algorithm w...

Implement the Prim's algorithm with array data structure as described in slide 12 of the file 04mst.ppt. Your program should have a runtime complexity of O(n2) and should be as eff

Draw the sequence diagram for the scenario, Draw the sequence diagram for t...

Draw the sequence diagram for the following scenario of eBroker. Sell Stock The user enters the username and password The system checks that the user is a valid user

Python , Return a new picture with each pixel''s color values made up of 80...

Return a new picture with each pixel''s color values made up of 80% of the color values of the corresponding pixel in the first picture and 20% of the color values of the

Write a complete program using floating-point operations, Question 1: a...

Question 1: a) Assume that B is an array of 50 words; write a code which will place the smallest integer of array B in register AX. b) Write a small code (only three instr

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd