AMV – 1A9
Formulate the LP problems (do not solve).
1. MD Electronics Corp. is planning to produce two products C13 and C15. At the assembly plant,
a C13 unit requires 4 hours and a C15 requires 5 hours. C13 and C15 units require 3 and 2
hours, respectively, for finishing. At most 220 hours and 210 hours of assembly and finishing,
respectively, are available per month. If the anticipated profit is P30/unit for C 13 and P25/unit
for C15, find the product mix to maximize the profit.
Decision Variables:
Objective Function:
Constraints:
Let x be the no. of units of product C13 and y the no.
of units of product C15
Maximize z = 30x +25y
Assembly plant: 4x + 5y ≤ 220
Finishing plant: 3x + 2y ≤ 210
Non-negativity constraint: x, y ≥ 0
2. ABC Furniture produces inexpensive tables and chairs. Both require labor hours for carpentry
and painting jobs. Each table requires 4 hours of carpentry time and 2 hours of painting time.
Each chair requires 3 hours of carpentry and 1 hour of painting time. During the production
period, there are 240 hours available for carpentry and 100 hours for painting. Each table
yields P150 profit and each chair, P75. Determine the best product combination to optimize
profit.
Decision Variables:
Let x be the no. of tables and y be the no. of chairs
Objective Function:
Maximize z = 150x + 75y
Constraints:
Carpentry: 4x + 3y ≤ 240
Painting: 2x + y ≤ 100
Non-negativity constraint: x, y ≥ 0
3. As part of quality improvement initiative, Consolidated Electronic employees complete a
three-day training program on team building and a two-day training program on problem
solving. The manager of quality improvement has requested that at least 8 training programs
on team building and at least 10 training programs on problem solving be offered during the
next six months. In addition, senior level management has specified that at least 25 training
programs must be offered during this period. The company uses a consultant to teach the
training programs. During the said period, the consultant has 48 days of training time
available.
Each training program on teaming costs P150,000 and each training program on problem
solving costs P125,000. Determine the number of training programs on team building and the
number of training programs on problem solving that should be offered in order to minimize
the total cost.
Decision Variables:
Objective Function:
Constraints:
Let x be the no. of team building training programs and y
be the no. of problem-solving training programs
Minimize z = 150,000x + 125,000y
Manager of QI (within the next six months): x ≥ 8
y ≥ 10
Senior Level Management: x + y ≥ 25
Consultant availability: 3x + 2y ≤ 48
Note: It is not necessary to include the non-negativity constraint in this case because the QI
manager’s request (first 2 explicit constraints) is non-negative in nature.
4. The New England Cheese Co. produces two cheese spreads by blending mild cheddar with
extra sharp cheddar cheese. The cheese spreads are packaged in 128-oz containers which
are then sold to distributors. The Regular blend contains 80% mild cheddar and 20% extra
sharp, and the Zesty blend contains 60% mild cheddar 40% extra sharp. This year, a local
dairy cooperative offered to provide up to 8,100 lbs of mild cheddar cheese for P54 per lb
and up to 3,000 lbs of extra sharp cheddar cheese for P63 per lb. The cost to blend and
package the cheese spreads, excluding the cost of cheese, is P9 per container.
If each container of Regular is sold for P700 and each container of Zesty is sold for P750,
how many containers of Regular and Zesty should New England Cheese produce in order to
maximize the profit?
Note: It is necessary to convert the unit of measurement of some quantities. We may use the
conversion 16 oz = 1 lb. Hence, the cheese spreads are packaged in 8-lbs container.
In the formulation, it will be helpful to create a table of the values given:
Products
in containers
Regular Blend
Zesty Blend
Availability
Ingredients
Mild
Extra
Cheddar
Sharp
80%
60%
≤ 8100 lbs
Decision Variables:
Objective Function:
Constraints:
20%
40%
Total Cost of
Ingredients
per container
Cost to Blend
and Package,
in PhP
Selling Price,
in PhP
Profit per
container
446.4
460.8
9
9
700
750
244.6
280.2
≤ 3000 lbs
Let x be the no. of containers of regular blend cheese
And y be the no. of containers of zesty blend cheese
Maximize z = 244.6x + 280.2y
Mild Cheddar: 6.4x + 4.8y ≤ 8,100
Extra Sharp: 1.6x + 3.2y ≤ 3,000
Non-negativity constraint: x, y ≥ 0
5. A nutritionist advises an individual who is suffering from iron and vitamin-B deficiency to take
at least 2400 mg of iron, 2100 mg of vitamin B1 and 1500 mg of vitamin B2 over a certain
period of time. Two vitamin capsules are suitable, Neuro-Iron and Sango-Iron. Each NeuroIron capsule costs P6 and contains 40 mg of iron, 10 mg of vitamin B1 and 5 mg of vitamin
B2. Each Sango-Iron costs P8 and contains 10 mg of iron and 15 mg each of vitamins B1
and B2. What combination of each brand should the individual purchase in order to meet the
minimum iron and vitamin requirements at the lowest cost?
Decision Variables:
Objective Function:
Constraints:
Let x be the no. of Neuro-Iron vitamin capsules and y
be the no. of Sango-Iron vitamin capsules
Minimize z = 6x + 8y
Iron: 40x + 10y ≥ 2,400
Vitamin B1: 10x + 15y ≥ 2,100
Vitamin B2: 5x + 15y ≥ 1,500
Non-negativity constraint: x, y ≥ 0
6. Moonlife Financials has a total of P100 million earmarked for home and auto loans. On the
average, home loans have a 10% annual rate of return while auto loans yield a 12% annual
rate of return. Management also stipulated that the total amount of home loans should be
greater than or equal to 4 times the total amount of automobile loans. Determine the total
amount of loans for each type Moonlife Financials should extend to each category in order to
maximize its returns.
Decision Variables:
Objective Function:
Constraints:
Let x be the amount of home loans and y be the
amount of auto loans
Maximize z = 0.1x + 0.12y
Management Stipulation: x ≥ 4y
Amount earmarked for loans: x + y ≤ 100,000,000
Non-negativity constraint: x, y ≥ 0
7. As part of a campaign to promote its annual clearance sale, Shangri-Son Malls decided to
buy television advertising time on Station ABS-5. Its advertising budget is P5 million. Morning
time costs P150,000/minute, afternoon time costs P50,000/minute and evening or prime time
costs P600,000/minute. Station ABS-5 cannot offer Shangri-Son Malls more than 6 minutes
of prime time or more than a total of 25 minutes of advertising time over the weeks in which
the commercials are to be run. Station ABS-5 estimates that morning commercials are seen
by 200,000 people, afternoon commercials are seen by 100,000 people while evening
commercials are seen by 600,000 people. How much morning, afternoon and evening
advertising time should Shangri-Son Malls buy in order to maximize exposure of its
commercials?
Decision Variables:
Objective Function:
Constraints:
Let x be the no. of minutes of morning time
y be the no. of minutes of afternoon time; and
z be the no. of minutes of evening/primetime
Maximize exposure (e) = 200,000x + 100,000y +
600,000z
Advertising budget: 150,000x + 50,000y + 600,000z ≤
5,000,000
Minutes of Primetime: z ≤ 6
Advertising time over the weeks: x + y + z ≤ 25
Non-negativity constraint: x, y, z ≥ 0