Question

A plant assembles chairs and tables. The average assembly times are 20 minutes/chair. Sales

forecasts for the next three months are given in the table.

Product March April Current inventory

Chair 2800 2300 30

Table 500 800 100

The production costs and the selling prices for the products are shown next.

Product Unit cost Unit price

Chair $150/chair $250/chair

table $400/table $750/table

Monthly inventory charges are 2% of the production cost.

The workforce will be available up to 32000 hours / month

3. a) Please formulate above scenario as LP for minimizing the total production costs.

First, define your decision variables, and then use them in your LP model.

3. b) Please solve the LP model you created on

define your decision variables, then objective function and constraints.

Answer #1

a) LP model is as follows

Let C1, C2 and T1, T2 be the number of Chairs and Tables to produce in month of March and April respectively

VC and VT be the inventory of Chairs and Tables in March

Objective: Max (250-150)*(C1+C2)+(750-400)*(T1+T2)-150*2%*VC-400*2%*VT

s.t.

(20/60)*(C1+T1) <= 32000

(20/60)*(C2+T2) <= 32000

C1-VC = 2800-30

C2+VC = 2300

T1-VT = 500-100

T2+VT = 800

All variables >= 0

b) Solution of LP model is following

Solution:

Chairs to be produced in March (C1) = 2770

Chairs to be produced in March (C2) = 2300

Tables to be produced in March (T1) = 400

Tables to be produced in March (T2) = 800

Optimal value = $ **807,000**

4) A furniture manufacturing company manufactures tables and
chairs. The relevant
manufacturing data are given in the table below. How many tables
and chairs should be manufactured each day to maximize profit? (12
POINTS)
Note: Please clearly define your variables and indicate the
objective function and the constraints. Indicate the scale of your
axes, and write your final answer using a complete sentence with
correct units.
Department
Table Labor-Hours per Unit
Chair Labor-Hours per Unit
Maximum Labor-Hours Available per Day...

Part 3 – Steelcase Production
Steelcase Corporation manufactures 3 basic products: chairs,
desks, and tables. Below is chart which summarizes the number of
labor hours spent for each product in each division.
Chairs
Desks
Tables
Process
Carpentry
2
3
6
Finishing
1
1
1
Assembly
4
6
2
In a given week, Steelcase has 250 hours available for
carpentry, 100 hours available for finishing, and 400 hours
available for assembly.
Steelcase makes a profit of $66 on each chair, $75...

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...

A company produces a certain product and has the capacity to
produce 100 units per month in regular time, and an additional 15
units per month in overtime. The production cost of the product
varies by month due to changes in the material costs over time. The
quantities of the product to be delivered over the next six months
have already been set. The delivery requirements and production
costs are given in the following table:
Month
1
2
3
4...

Utopia Company operates a plant in Avalon with a monthly
capacity of 35,000 units and a plant in Bridgetown with a monthly
capacity of 40,000 units. Product is shipped to regional
distribution centers located in Riverdale, Seaside and Teatown.
The long-range planning group at Utopia reevaluated their
forecasts and determined that due to an anticipated increase in
demand in the next 5 years, the company should consider
increasing capacity by constructing a new plant in one or
more of the...

The Silver Star Bicycle Company will manufacture both men's and
women's models for its Easy-Pedal bicycles during the next two
months. Management wants to develop a production schedule
indicating how many bicycles of each model should be produced in
each month. Current demand forecasts call for 150 men's and 125
women's models to be shipped during the first month and 200 men's
and 150 women's models to be shipped during the second month.
Additional data are shown: Labor Requirements (hours)...

Muzi Corporation produces three products at two different
plants. The cost of producing a unit at each plant is given in the
following table.
Product 1
Product 2
Product 3
Plant A
R5
R6
R8
Plant B
R8
R7
R10
Each plant has the capacity to produce a total of 10 000 units.
Demand for at least 6 000 units of product 1, at least 8 000 units
of product 2 and at least 5 000 units of product 3...

Need to see step by step solutions Please:
Solve Problem and Applications: ch 13- prob 7
[Klein Industries manufactures three types of portable air
compressors] in page 451 at the end of chapter 13 in your textbook,
USA 5th edition. The data is given as part of the question. There
is no external data set provided. Use what is given by the problem.
You need to submit a formal APA paper to explain all your
findings together with your Excel...

Answer Questions 2 and 3 based on the following LP
problem.
Let P1 = number of Product 1 to be
produced
P2 =
number of Product 2 to be produced
P3 =
number of Product 3 to be produced
Maximize 100P1 + 120P2 +
90P3 Total
profit
Subject to
8P1 + 12P2 + 10P3 ≤
7280 Production budget
constraint
4P1 + 3P2 + 2P3 ≤ 1920 Labor
hours constraint
P1
> 200 Minimum
quantity needed...

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