Question

1. A firm produces four products: Each unit of product 1 requires two hours of assembly, one hour of painting and $50 of inventory, Each unit of product 2 requires one hour of assembly, three hours of painting and $75 of inventory, Each unit of product 3 requires 2.5 hours of assembly, 2.5 hours of painting and $20 of inventory, Each unit of product 4 requires 5 hours of assembly no painting and $100 of inventory. The firm has 140 hours of assembly time and 200 hours of painting time available. They also can not have more than $100,000 tied up in inventory. Each unit of product 1 returns a profit of $40, each unit of product 2 returns $30, each unit of product 3 returns $37 and each unit of product 4 returns $25. Not more than 20,000 units of product 1 can be sold, not more than 16,000 units of product 3 can be sold and there are no limits on the sale of products 2 and 4. We must however produce a minimum of 15,000 units of product 4 to fulfill a Gov. Contract. Formulate and LP model to maximize profit.

Answer #1

Choosing the Optimal Product Mix with One Constrained
Resource
Billings Company produces two products, Product Reno and Product
Tahoe. Each product goes through its own assembly and finishing
departments. However, both of them must go through the painting
department. The painting department has capacity of 1,650 hours per
year. Product Reno has a unit contribution margin of $125 and
requires five hours of painting department time. Product Tahoe has
a unit contribution margin of $52 and requires two hours of...

A firm produces three products: A, B, and C. Each requires 3
resources in the production process: 1, 2, and 3. There are 15,000,
units of resource 1 available. There are 17,000 units of resource 2
available. There are 19,000 units of resource 3 available. Product
A requires 4 units of resource 1, 3 units of resource 2, and 5
units of resource 3. Product B requires 7 units of resource 1, 6
units of resource 2, and 5 units...

A firm produces three products: A, B, and C. Each requires 3
resources in the production process: 1, 2, and 3. There are 15,000,
units of resource 1 available. There are 17,000 units of resource 2
available. There are 19,000 units of resource 3 available. Product
A requires 4 units of resource 1, 3 units of resource 2, and 5
units of resource 3. Product B requires 7 units of resource 1, 6
units of resource 2, and 5 units...

1) MNO produces a single product. The standard production
requirement for each unit requires 0.50 direct labour hours at a
standard rate of $11 per hour. During the last year, MNO assembly
line workers worked a total of 5,000 hours at a cost of $50,000 to
MNO. Also last year, MNO manufactured 3,000 units of product. What
was the company's direct labour rate variance for the year?
2) MNO produces a single product. The standard production
requirement for each unit...

The Wellbuilt Company produces two types of wood chippers,
economy and deluxe. The deluxe model requires 3 hours to assemble
and 1 2 hour to paint, and the economy model requires 2 hours to
assemble and 1 hour to paint. The maximum number of assembly hours
available is 24 per day, and the maximum number of painting hours
available is 8 per day. If the profit on the deluxe model is $90
per unit and the profit on the economy...

Choosing the Optimal Product Mix with a Constrained Resource and
a Demand Constraint
Billings Company produces two products, Product Reno and Product
Tahoe. Each product goes through its own assembly and finishing
departments. However, both of them must go through the painting
department. The painting department has capacity of 2,460 hours per
year. Product Reno has a unit contribution margin of $120 and
requires 5 hours of painting department time. Product Tahoe has a
unit contribution margin of $75 and...

The Wellbuilt Company produces two types of wood chippers,
economy and deluxe. The deluxe model requires 3 hours to assemble
and 1/2 hour to paint, and the economy model requires 2 hours to
assemble and 1 hour to paint. The maximum number of assembly hours
available is 24 per day, and the maximum number of painting hours
available is 8 per day. If the profit on the deluxe model is $94
per unit and the profit on the economy model...

hoosing the Optimal Product Mix with a Constrained Resource and
a Demand Constraint
Billings Company produces two products, Product Reno and Product
Tahoe. Each product goes through its own assembly and finishing
departments. However, both of them must go through the painting
department. The painting department has capacity of 2,460 hours per
year. Product Reno has a unit contribution margin of $120 and
requires five hours of painting department time. Product Tahoe has
a unit contribution margin of $75 and...

The Electrotech Corporation manufactures two industrial-sized
electrical devices: generators and alternators. Both of these
products require wiring and testing during the assembly process.
Each generator requires 2 hours of wiring and 1 hour of testing and
can be sold for a $250 profit. Each alternator requires 3 hours of
wiring and 2 hours of testing and can be sold for a $150 profit.
There are 260 hours of wiring time and 140 hours of testing time
available in the next...

10) Natural Furniture Company manufactures three outdoor
products, chairs, benches, and tables. Each product must pass
through the following departments before it is shipped: sawing,
sanding, assembly, and painting. The time requirements (in hours)
are summarized in the tables below.
The production time available in each department each week and
the minimum weekly production requirement to fulfill contracts are
as follows:
Minimum
Capacity
Production
Department
(In Hours)
Product
Level
Sawing
450
Chairs
100
Sanding
400
Benches
50
Assembly
625
Tables...

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