BUS 190 Homework 2

BUS 190        Homework 2

For this week’s homework, you will just be asked to set up the linear program as we did in class, and then to rewrite it in the ‘algebraic form’.  Homework 3 will involve graphing the constraints and solving the linear program using that graph, so if you want to get a head start on Homework 3 and are sure of your algebraic setup, you can start the graphs. DO NOT INCLUDE graphs here on HW 2.

  1. Suppose a small company is in the business of making golf bags to be sold at a local golf course where state championships are often held. They make 2 types of golf bags, a standard bag and a deluxe bag.  The table below gives the information for limitations of materials and labor hours, and also for the profit for each type of bag.  The materials and labor hours are the number of hours available per week, and the profit is the profit in $ per week as well.

Units are per bag

Standard Leather (square feet)

Premium Leather (square feet)

Cutting and Sewing Labor hours

Finishing Labor Hours

Profit ($)

Standard

 7

1

3

1

25

Deluxe

 0

9

4

2

65

Total available

 210

180

120

40

  1. What are the decision variables (use NUN!)

The decision variables are S for the number of standard bags and D for the number of deluxe bags.

  1. What is the objective function? (make sure to use dimensional analysis to set it up)

The objective function is to maximize profit. The formula is max (z) = 25S + 65D.

$25                            S of standard bags                     $65           D of deluxe bags

--------                  *                                             +            -------     *                         = $25S + $65D

1 standard bag                                                                 1 deluxe bag

  1. What are the constraints? Make sure to use dimensional analysis to set them up.

The constraints are:

7           * S standard leather sq ft          0 * D standard leather sq ft             

-----                                                       +        -------                                         <= 210

1 standard leather sq ft                        standard leather sq ft                           

1           * S premium leather sq ft          9 *D premium leather sq ft             

-----                                                       +        -------                                         <= 180

1 premium leather sq ft                        premium leather sq ft                          

3           * S cslabor hours          4 * D cslabor hours             

-----                                                       +        -------                                         <= 120

1 cslabor hours                        cslabor hours                           

1          * S flabor hours          1 * D flabor hours   

-----                                                       +        -------                                         <= 140

1 flabor hours                           flabor hours                              

7S+0D <= 210

1S + 9D <= 180

3S + 4D <= 120

1S + 1D <= 40

  1. Summarize the linear program in algebraic form. You do not need to include units here, but you should label your constraints.

Z = 25S + 65D

s.t.

standard leather constraint: 7S+0D <= 210

premium leather constraint: 1S + 9D <= 180

cutting and sewing labor hours constraint: 3S + 4D <= 120

finished labor hours constraint: 1S + 1D <= 40

And

S >= 0, D >= 0

  1. You have just inherited $100,000 from a relative, and you want to invest the money so that you get the maximum annual return you can.  You are thinking of putting your money into two types of stock mutual funds. One fund S concentrates in social media companies, and the other fund I concentrates in companies that specialize in infrastructure construction and maintenance.  You also are sensitive to risk in investment, so you visited a financial consultant to determine your risk tolerance.   You are also worried that since social media isn’t a tangible product, you want to limit the number of shares you own in that mutual fund to be less than 1000. The table below summarizes the information you have at hand, per share.

Cost ($)  per share

Risk (unitless)

Max shares

Expected annual return ($1,000s)

Social media

$50

0.5

1

5

Infrastructure

$30

0.25

7

Total

$100,000

700

1000

  1. What are the decision variables (use NUN!)

The decision variables are S as the number of units purchased in fund S and I as the number of units purchased in fund I.

  1. What is the objective function? (make sure to use dimensional analysis to set it up)

The objective function is maximizing expected annual return (z) = 5S + 7I

5S          * 1 shares            7I *  shares

--------                  +             -------                   = 5S + 7I

1 share                              1 share

  1. What are the constraints? Make sure to use dimensional analysis to set them up.

5           * S shares             $30 * I shares

--------                  +             -------                   <= $100,000

1 share                              1 share

1S shares <= 1000 shares

$50S + $30I <= $100000

S <= 1000

.5S + 0.25I <= 700

  1. Summarize the linear program in algebraic form. You do not need to include units here, but you should label your constraints.

z = maximized expected annual return

z = 5S + 7I

s.t.

cost constraint: 50S + 30I <= 100000

max shares constraint: S <= 1000

risk restraint: .5S + 0.25I <= 700

S >= 0, I >= 0

  1. Suppose you are in the business of manufacturing white board markers. You make two types: Standard and Heavy Duty. You sell these to wholesalers for $10/box of 10 for Standard Markers and $15/box of 10 for Heavy Duty markers. Each standard marker is made up of 3 oz. of plastic and 1 fl. Oz. of marker fluid. Each Heavy Duty Marker is made up of 5 oz. of plastic and 1.5 fl. oz of marker fluid.   Plastic costs $1/lb and marker fluid costs $5/gal.  Each marker takes 30 seconds to manufacture by machine, but the machine can manufacture up to 10 at one time. Machine time costs $60/hr.

Set up the profit function for each type of marker, USING DIMENSIONAL ANALYSIS as you would have to do for a linear program objective function where you wanted to maximize profit.  It is probably easiest to figure out profit per marker rather than profit per box, but you may use either unit, as long as you are consistent and use the same unit throughout the entire problem.  SHOW ALL YOUR WORK TO GET CREDIT. Warning: do NOT skip using units at any stage. Numbers multiplied together without units in intermediate calculations, but  with units attached to them at the end will earn you ZERO points, even if your ‘number’ is correct.

Profit function ($) = (1-(.2665625+.05))x + ((10/15)-(.37190375+.05))y

  1. Consider the following linear program

Max 1A + 1B

  1. t.

5A + 3B ≤ 15

3A + 5B ≤ 15

A, B ≥ 0

Graph the two constraints and find the overall feasible region for the problem.  You should use the original large block graph paper I handed out first day of class and use 2 blocks per unit.

Constraint 1

5A + 3B ≤ 15

0A + 3B ≤ 15 and 5A +0B ≤ 15

B = 5

A = 3


Constraint 2

3A + 5B ≤ 15

0A + 5B ≤ 15 and 3A +0B ≤ 15

A = 5

B = 3

Test point for both (0,0)

0*5 + 0*3 ≤ 15, Correct

0*3 + 0*5 ≤ 15, Correct

hihi

Download Sample Now

Earn back money you have spent on downloaded sample



Upload Document Document Unser Evaluion Get Money Into Your Wallet



Cite This work.

To export a reference to this article please select a referencing stye below.

Assignment Hippo (2021) . Retrive from http://assignmenthippo.com/sample-assignment/bus-190-homework-2

"." Assignment Hippo ,2021, http://assignmenthippo.com/sample-assignment/bus-190-homework-2

Assignment Hippo (2021) . Available from: http://assignmenthippo.com/sample-assignment/bus-190-homework-2

[Accessed 19/10/2021].

Assignment Hippo . ''(Assignment Hippo,2021) http://assignmenthippo.com/sample-assignment/bus-190-homework-2 accessed 19/10/2021.


Want latest solution of this assignment

Want to order fresh copy of the Sample Template Answers? online or do you need the old solutions for Sample Template, contact our customer support or talk to us to get the answers of it.


Submit Your Assignment Here

AssignmentHippo Features

On Time Delivery

Our motto is deliver assignment on Time. Our Expert writers deliver quality assignments to the students.

Plagiarism Free Work

Get reliable and unique assignments by using our 100% plagiarism-free.

24 X 7 Live Help

Get connected 24*7 with our Live Chat support executives to receive instant solutions for your assignment.

Services For All Subjects

Get Help with all the subjects like: Programming, Accounting, Finance, Engineering, Law and Marketing.

Best Price Guarantee

Get premium service at a pocket-friendly rate at AssignmentHippo

FREE RESOURCES

  • Assignment Writing Guide
  • Essay Writing Guide
  • Dissertation Writing Guide
  • Research Paper Writing Guide

FREE SAMPLE FILE

  • Accounts
  • Computer Science
  • Economics
  • Engineering

Client Review

I was struggling so hard to complete my marketing assignment on brand development when I decided to finally reach to the experts of this portal. They certainly deliver perfect consistency and the desired format. The content prepared by the experts of this platform was simply amazing. I definitely owe my grades to them.

Tap to Chat
Get instant assignment help