Problem 1 I'm tired of being a professor. My latest scheme to get rich quickly is to produce a variety of cookies for consumption by calls for the production of three types of cookies - Primal Biscotti, Dual Shortbread, and Simplex Cracker. I know that each box of Primal Biscotti produced will yield $15 profit, cach box of Dual Shortbread yields $40 profit, and each box of Simplex Cracker produced gives $60 profit. In order to produce cookies, two raw materials are required: Sugar and Flour. I have a limited supply of each of these materials: My business plan Materials Amount (lbs) Suger 60 Flour 20 In order to produce a box, each type of the cookies requires a certain amount of each of the two raw materials: Cookie Sugar Flour Primal Biscotti 15 Dual Shortbread 20 Simplex Cracker 15 (a) Formulate a linear program that will maximize my profit. You may assume that I will sell all cookies produced, even fractional amounts. Use the following decision variables in your linear program: x1: # of boxes of Primal Biscotti produced r2: # of boxes of Dual Shortbread produced 23: # of boxes of Simplex Cracker produced (b) Convert the linear program in (a) into the standard form by introducing two slack variables s1 and s2, one for each resource limit constraint. (c) Solve the standard form linear program in (b) by the simplex algorithm. Display the final optimal tableau below.
Problem 1 I'm tired of being a professor. My latest scheme to get rich quickly is to produce a variety of cookies for consumption by calls for the production of three types of cookies - Primal Biscotti, Dual Shortbread, and Simplex Cracker. I know that each box of Primal Biscotti produced will yield $15 profit, cach box of Dual Shortbread yields $40 profit, and each box of Simplex Cracker produced gives $60 profit. In order to produce cookies, two raw materials are required: Sugar and Flour. I have a limited supply of each of these materials: My business plan Materials Amount (lbs) Suger 60 Flour 20 In order to produce a box, each type of the cookies requires a certain amount of each of the two raw materials: Cookie Sugar Flour Primal Biscotti 15 Dual Shortbread 20 Simplex Cracker 15 (a) Formulate a linear program that will maximize my profit. You may assume that I will sell all cookies produced, even fractional amounts. Use the following decision variables in your linear program: x1: # of boxes of Primal Biscotti produced r2: # of boxes of Dual Shortbread produced 23: # of boxes of Simplex Cracker produced (b) Convert the linear program in (a) into the standard form by introducing two slack variables s1 and s2, one for each resource limit constraint. (c) Solve the standard form linear program in (b) by the simplex algorithm. Display the final optimal tableau below.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 1 I'm tired of being a professor. My latest scheme to get rich quickly is to produce a
variety of cookies for consumption by G
calls for the production of three types of cookies – Primal Biscotti, Dual Shortbread, and Simplex
Cracker. I know that each box of Primal Biscotti produced will yield $15 profit, each box of Dual
Shortbread yields $40 profit, and each box of Simplex Cracker produced gives $60 profit. In order
to produce cookies, two raw materials are required: Sugar and Flour. I have a limited supply of
My business plan
each of these materials:
Materials Amount (lbs)
Suger
60
Flour
20
In order to produce a box, each type of the cookies requires a certain amount of each of the two
raw materials:
Cookie
Sugar Flour
Primal Biscotti
15
Dual Shortbread
20
5
Simplex Cracker
15
(a) Formulate a linear program that will maximize my profit. You may assume that I will sell all
cookies produced, even fractional amounts. Use the following decision variables in your linear
program:
x1: # of boxes of Primal Biscotti produced
• x2: # of boxes of Dual Shortbread produced
• x3: # of boxes of Simplex Cracker produced
(b) Convert the linear program in (a) into the standard form by introducing two slack variables
s1 and s2, one for each resource limit constraint.
(c) Solve the standard form linear program in (b) by the simplex algorithm. Display the final
optimal tableau below.
(d) How much should I be willing to pay for one extra pound of Sugar?
(e) I am thinking of investing in a new cookie product, Basis Macaron. One box of Basis Macaron
requires 15 lbs of sugar and 10 lbs of flour. I can sell Basis Macaron for $40/box. Based on
the information that you obtain from the optimal tableau in part (c), is it worthy to invest
Basis Macaron? Justify your answer.
(f) What is the range of values (“safety zone") for the amount of sugar so that the optimal basis
does not change? Note that the current amount of sugar is 60.
(g) How much can you increase the profit for Primal Biscotti while the current optimal solution
stays optimal? Why?
(h) Suppose Costco has sugar on sale next week. Their offer is $100 for a bag (50 lbs). Should I
accept this offer? Why?
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