Math 280 – Introduction to Probability and Statistics
Module 11 Application Assignment (16 Points)
This assignment has 32 points in total. Your score will be divided by two to find your actual assignment score for the gradebook.
MAXIMIZING PROFIT: CUSTOM GAMING PCs
You are the owner of a mid-sized computer manufacturing and assembling facility – what started as a small business building and customizing computers for friends and family has grown into a much larger operation, and you want to make sure you are using your labor hours in the most efficient way to maximize your profits. Your company manufactures and assembles three types of custom gaming PCs, and the amount of manufacturing and assembling times required for each model along with the profit you make on each unit are given below:
| Model Name | Manufacturing Time (in hours) | Assembling Time (in hours) | Profit (per unit sold) |
| Dendrite Ice | 2 | 2 | $280 |
| Neuron Pro | 3 | 2 | $320 |
| Axon Glacier Pro | 2 | 4 | $400 |
Your labor budget each week is 1,000 hours of total manufacturing time, and 1,600 hours of assembly time. How many of each type of custom gaming PC should you task your teams with creating each week to maximize your profit?
1. (6 points) Identify the variables you are solving for in this problem (assign a letter name and describe each in word) and write down the constraints of the problem using inequalities (include any ‘natural’ constraints as well).
2. (3 points) Write down an equation for the objective function you are trying to maximize (profit). Then, rewrite this equation into the form of an inequality that you will use to enter it into the simplex tableau.
4. (5 points) Fill in the initial simplex tableau for this problem below (each blank cell in the table should contain a variable letter or a numeric value when you are finished):
5. (9 points)Simplify the simplex tableau above, systematically removing all negative values in the bottom row, by pivoting and using appropriate row operations. Below show EACH new tableau step (hint: there should be three steps, blank tableaus provided). At each step, indicate the row operations you used, the element of the tableau you used to pivot and why you pivoted on that element of the tableau.
Describe first step (then fill in revised tableau with new values):
Describe second step (then fill in revised tableau with new values):
Describe third step (then fill in revised tableau with new values):
6. (6 points) Provide the solution to your completed tableau, listing the values for each variable (including any slack variables) and the objective function. Finally, state the solution in terms of our original problem: how many of each type of custom gaming PC should your teams manufacture each week in order to maximize your profits?
- (3 points) In your own words, explain what a Linear Programming problem is with all of its components.
