Briley Cosmetics manufactures and distributes a wide range of skin care products. A recent order has arrived for 10,000 cartons of face cream, 5,000 cases of body cream, and 15,000 cases of hand cream. The manufacturing process consists of a two-stage procedure that uses two types of raw materials (A and B). Briley's monthly production capacity (first shift) is 15,000 labor-hours for stage 1 and 10,000 for stage 2. The first shift hourly rates are $8.50 for stage 1 and $9.25 for stage 2. A second shift is available with a 10% reduction in capacity and a 10% increase in wage rates. The cost for raw materials is $1/pound for Type A and $1.50/pound for Type B. The manufacturing facility has available for the next production run 200,000 pounds of Type A and 150,000 pound of Type B. The following table summarizes the resource requirements to produce each product.

Briley Cosmetics manufactures and distributes a wide range of skin care products. A recent order has arrived for 10,000 cartons of face cream, 5,000 cases of body cream, and 15,000 cases of hand cream. The manufacturing process consists of a two-stage procedure that uses two types of raw materials (A and B). Briley's monthly production capacity (first shift) is 15,000 labor-hours for stage 1 and 10,000 for stage 2. The first shift hourly rates are $8.50 for stage 1 and $9.25 for stage 2. A second shift is available with a 10% reduction in capacity and a 10% increase in wage rates. The cost for raw materials is $1/pound for Type A and $1.50/pound for Type B. The manufacturing facility has available for the next production run 200,000 pounds of Type A and 150,000 pound of Type B. The following table summarizes the resource requirements to produce each product.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Briley Cosmetics Inc.
Briley Cosmetics manufactures and distributes a wide range of skin care products. A
recent order has arrived for 10,000 cartons of face cream, 5,000 cases of body cream,
and 15,000 cases of hand cream. The manufacturing process consists of a two-stage
procedure that uses two types of raw materials (A and B). Briley's monthly production
capacity (first shift) is 15,000 labor-hours for stage 1 and 10,000 for stage 2. The first
shift hourly rates are $8.50 for stage 1 and $9.25 for stage 2. A second shift is available
with a 10% reduction in capacity and a 10% increase in wage rates. The cost for raw
materials is $1/pound for Type A and $1.50/pound for Type B. The manufacturing
facility has available for the next production run 200,000 pounds of Type A and 150,000
pound of Type B. The following table summarizes the resource requirements to produce
each product.
Face
Body
Cream
Hand
Cream
Cream
Labor (hr/carton)
Stage 1
Stage 2
Raw Materials
1.5
1.8
1.0
0.8
1.0
0.5
(Ib/carton)
A
5.0
8.0
3.0
В
7.0
4.0
9.0
Briley can also subcontract with a local supplier for face cream and body cream at a
cost of $40/carton and $55/carton, respectively.
1. What production schedule minimizes total cost while meeting product demand?
2. How much face cream and body cream is subcontracted out?
3. What is the value of the objective function?

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Briley Cosmetics manufactures and distributes a wide range of skin care products. A recent order has arrived for 10,000 cartons of face cream, 5,000 cases of body cream, and 15,000 cases of hand cream. The manufacturing process consists of a two-stage procedure that uses two types of raw materials (A and B). Briley's monthly production capacity (first shift) is 15,000 labor-hours for stage 1 and 10,000 for stage 2. The first shift hourly rates are $8.50 for stage 1 and $9.25 for stage 2. A second shift is available with a 10% reduction in capacity and a 10% increase in wage rates. The cost for raw materials is $1/pound for Type A and $1.50/pound for Type B. The manufacturing facility has available for the next production run 200,000 pounds of Type A and 150,000 pound of Type B. The following table summarizes the resource requirements to produce each product. Face Body Cream Hand Cream Cream Labor (hr/carton) Stage 1 Stage 2 Raw Materials 1.5 1.8 1.0 0.8 1.0 0.5 (Ib/carton) A 5.0 8.0…
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