Case Study $1$: Ace Manufacturing $-$ Maximizing Profit in Backpack Production

Case Summary

Ace Manufacturing is a small business specializing in premium sports accessories. Recently, the company decided to expand its product line to include two types of premium backpacks: Basic and Advanced models. Ace Manufacturing has a committed buyer who is willing to purchase as many backpacks as they can produce within the next quarter. To maximize its profit, Ace Manufacturing needs to determine the optimal number of each type of backpack to produce.

Manufacturing Process

The production process for each backpack type involves four main stages:

$1.$ Material Preparation $-$ Cutting and dyeing fabric.

$2.$ Assembly $-$ Stitching and assembling materials.

$3.$ Finishing Touches $-$ Adding components such as straps and zippers.

$4.$ Quality Check and Packaging $-$ Inspecting and packing the final product.

Production Parameters

Stage

Basic Backpack $($hrs$)$

Advanced Backpack $($hrs$)$

Available Hours

Material Preparation

$7/10$

$1$

$630$

Assembly

$1/2$

$5/6$

$600$

Finishing Touches

$1$

$2/3$

$708$

Quality Check and Packaging

$1/10$

$1/4$

$135$

Profit per Backpack

The profit per backpack for each model is as follows:

Backpack Type

Profit per Backpack $($$$)$

Basic

$12$

Advanced

$10$

Problem Formulation

To determine the optimal number of Basic and Advanced backpacks to produce, we need to set up a linear programming model. The objective is to maximize total profit.

Mathematical Model

Objective: Maximize total profit by finding the optimal production quantities for Basic $($B$)$ and Advanced $($A$)$ backpacks.

Decision Variables

B: Number of Basic backpacks produced

A: Number of Advanced backpacks produced

Objective Function

Maximize profit, Z $=12$B $+10$A

$$Questions

The following $8$ questions are designed to test your understanding of linear programming concepts, for the Ace Manufacturing case study, and how to solve the problem in Excel using Solver. Answer the questions based on the given case details.

What is the objective of Ace Manufacturing's linear programming model?

A$)$ Minimize production time

B$)$ Minimize total cost

C$)$ Maximize total profit contribution

D$)$ Maximize production quantity

E$)$ None of the above

Group of answer choices

A

B

C

D

E

$$

Flag question: Question $2$

Question $20\mathrm{.}4$ pts

How many hours remain unused, if any, in the Quality Check and Packaging department after producing the optimal number of backpacks?