Freddy González Suárez1

TECHNOLOGICAL UNITS OF SANTANDER -

Business Administration
In-depth Activity: Programming of Productive Operations POP - Linear Programming
Specific Competence to evaluate: Formulation of Linear Programming models for resolution
of relevant decision-making problems in the organization, in search of optimization in the allocation of
resources, production planning, transportation route optimization, and inventory management.
Objective: To master the formulation and application of Linear Programming (LP) models to address
critical challenges of decision-making within an organization, with the aim of achieving the
optimization in resource allocation, production planning, route optimization
transport and inventory management.
From the following exercises, select 5 of them; for each case, formulate a model of
linear programming that allows determining the maximum possible profit, or the maximum production
as applicable.
Develop 5 exercises of your choice on graph paper, representing them graphically.
each of the restrictions and marking the target area.

A business administration student wants to start a clothing business in partnership with

a fashion design student, developing modeling and design practices for garments, manages to
establish that, for the making of a dress, half an hour should be dedicated to cutting and 20 minutes
For the sewing or assembly of the garment; making a pair of pants takes 15 minutes.
Cut and half an hour for sewing or assembly. If the profit from a dress is $40,000 and that of a pair
The pants cost $90,000 and the business is operating a maximum of 8 hours a day. Determine
how many dresses and how many pairs of pants should be produced for maximum profit and
What is that benefit.
A agronomy student is looking for an 80-hectare piece of land on a farm in order to develop a
Agro-industrial project focused on the planting of corn and cabbages. It should cultivate at least 10 hectares of
corn and 20 cabbages to meet the demands. Prefers to plant more corn, but can only cultivate
up to three times more corn than cabbage. If the profit from corn is $8,000,000/ha and that from
coles $5,000.00 /ha, How should the farmer plant the two crops to achieve a profit?
maximum and what will that profit be?
3. The Technological Units of Santander UTS are preparing a trip for 400 students of
exchange with university in Baja California. The transport company has 10 aircraft of 50
available seats and 8 aircraft with 40 seats, but there are only 9 pilots available. The cost of the
An aircraft with 50 seats costs $8,000,000 and the one with 40 seats costs $6,000,000. Calculate.
how many aircraft of each type should they use to achieve the greatest possible benefit.
4. A transport company has two types of transport, A and B. Type A has a refrigerated chamber.
of 20 m3and a 40 m non-refrigerated area3, while type B has 30 m3in each section. A
Merchant needs to hire the service to transport 3,000 m.3from refrigerated stock and 4,000 m3of
not refrigerated. The cost per kilometer is $300,000 in vehicle type A and $400,000 in the vehicle
Type B. How many trucks of each type should be hired to achieve the lowest possible cost?
5. A business administration student, responsible for planning in sales in a
fashion store wants to liquidate 200 of its shirts and 200 of its pants from last season.
They have decided to make two offers, A and B. Offer A is a package that includes a shirt and a pair of
pants that will be sold for $300,000. Offer B is a package of three shirts and a pair of
pants that will be sold for $500,000. The store does not want to sell less than 20 packs of the
Offer A is no less than 10 of B. How many packages of each one does he need to sell to maximize the
money obtained from the promotion?
In a confectionery in Australia, famous for preparing two specialties of cake, the manager wishes to know
how many cakes can be made considering that the inventory has 10 kilos of sugar and
120 eggs. For this, it asks you to formulate a linear programming model that allows you to determine
the amount that can be produced of each of its specialties, to maximize its total profit.
If we consider that for a Sacher tart you need ½ kilo of sugar and 8 eggs and the Selva tart
Black requires 1 kilo of sugar and 8 eggs and sells them for 8 € and 10 € respectively.
a. State the problem and graphically represent the set of solutions.
b. What combinations of specialties can they make?
c. How many units of each specialty need to be produced to achieve the highest income for
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Type A oranges at $3,200 and type B at $4,500. How many kilograms of oranges?
How many of each type should be purchased to obtain maximum profit?
8. A goldsmith makes two types of jewelry. The unit of type A is made with 1 g of gold and 1.5
The type A weighs 2 grams of silver and is sold for $750,000. The type B is sold for $1,200,000 and contains 1.5 grams of gold.

and 1 g of silver. If you only have 750 g of each metal, how many pieces of jewelry must you make of
each type to obtain the maximum benefit?
A veterinary student is consulted to design a management plan.
food in a breeding facility if a minimum diet is to be provided to birds that consists of
3 units of iron and 4 units of vitamins daily. The student knows that each kilo of
corn provides 2.5 units of iron and 1 of vitamins and that each kilo of feed
the compound provides 1 kilogram of iron and 2 of vitamins. Knowing that the kilogram of corn
worth $5,000 and the compound feed $8,500, it is requested:
a. What is the composition of the daily diet that minimizes the farmer's costs?
Explain the steps taken to obtain the answer.
b. Would the solution to the problem change if the farmer does not due to market scarcity
Could I have more than 1 kilo of compound feed daily? Justify your answer.
A veterinary student is consulted to design a feeding plan.
for livestock in which a minimum daily supply of 4 mg of vitamin A must be provided and
6 mg of vitamin B in the food supplied to your cattle. You have available for this
two types of food P1y P2whose vitamin contents per kg are those that
they appear in the table:

A B
P1 2 6
P2 4 3

If the kilogram of P food1it costs $8,000 and the one from P2worth $12,000 how should they
mixing foods to supply the required vitamins at a cost
minimum?
11. An industrial engineering student in partnership with a mechanical engineering student.
automotive, they are going to organize a plant for a car workshop where they are going to
to work as electricians and mechanics. Considering the needs of the market and the
offer of skilled labor, it is necessary for there to be an equal or greater number of
mechanics than electricians and that the number of mechanics does not exceed double that of electricians.
of electricians. In total, there are 30 electricians and 20 mechanics available.
The company's profit per shift is $150,000 per electrician and $120,000 per
mechanic.
How many workers from each class should be chosen to achieve maximum benefit?
12. A person has $15,000,000 to invest in two types of stocks, A and B. The type
A has an annual interest of 9%, and type B has 5%. He decides to invest, at most,
$9,000,000 in A, and at least $3,000,000 in B. Additionally, he wants to invest in A.
as much as in B.
a. Draw the feasible region.
b. How should he invest the $15,000,000 for maximum benefit?
c. What is that maximum annual benefit?
13. A fashion design student has a sewing workshop where they manufacture
 Freddy González Suárez1

a pair of pants, $30.000.

Assuming that everything produced is sold, calculate the number of jackets.
and the pants that need to be made in order to achieve maximum profit.
14. A craftsman makes necklaces and bracelets. It takes him two hours to make a necklace and to make a
bracelet one hour. The material he has does not allow him to make more than 50 pieces.
At most, the craftsman can dedicate 80 hours to work. For each necklace, he earns
$25,000 and for each bracelet $20,000. The artisan wishes to determine the number of
necklaces and bracelets that should be manufactured to optimize profits.
Express the objective function and the constraints of the problem.
b. The defined area is represented graphically.
c. Obtain the number of necklaces and bracelets corresponding to the maximum
benefit.
15. In the UTS cafeteria, prepared meals are served; they ask a student to
administration that designs a menu using two ingredients. Ingredient A
it contains 35 g of fat and 150 kilocalories per 100 g of ingredient, while
Product B contains 15 g of fat and 100 kilocalories per 100 g. The cost is $6.00.
for every 100 g of ingredient A and $4,000 for every 100 g of ingredient B.
The menu to be designed should contain no more than 30 g of fats and at least 110.
Kilocalories per 100 g of food. It is requested to determine the proportions of each
ingredient to be used in the menu in a way that its cost is as low as possible.
a. Indicate the expression of the constraints and the objective function.
b. Graphically represent the region bounded by the restrictions.
c. Calculate the optimal percentage of each ingredient to include in the menu.
16. The business administration students want to paint the classrooms on the 5th floor;
minimum painting area corresponds to 480 m2You can buy the paint from two suppliers,
A and B. Supplier A offers you paint with a yield of 6 m.2per gallon and
a price of $60,000 per gallon. The paint from supplier B has a price of $80,000
per gallon and a yield of 8 m2No supplier can provide you with more than 75.
gallons and the painter's maximum budget is $1,200.00
Calculate the amount of paint that the students must buy from each supplier to
obtain the minimum cost. Calculate this minimum cost.

17. Determine the values of a and b so that the objective function F(x,y) = 3x + y
it reached its maximum value at the point (6, 3) of the feasible region defined by:
R1 = x 0
R2= y 0
R3= x + ay 3
R4= 2 x + y b
Represent the feasible region for those values and calculate the coordinates of
all its vertices.
18. An animal food factory produces a maximum of six daily.
tons of food of type A and a maximum of four tons of food of the
type B. Furthermore, the daily food production of type B cannot exceed the
double that of type A and, finally, double the production of food of type
The sum with type B must be at least four tons daily. Having
 Freddy González Suárez1

B. Food A contains 2 units of protein and 3 units of fat per

kilogram, while Food B contains 4 units of each of them
per kilogram. The farm needs to feed its chickens a total of 100
units of protein and 160 units of fat. The cost of the 50-kilogram bundle
The cost of Food A is $200,000 and the cost of the 50-kilogram sack of Food B
it is $300,000. Formulate a linear programming model to determine
how many kilograms of each type of food should the farm use to minimize the
total cost of food.
20. An advertising company has a budget to place ads in two media:
television and radio. The cost of a 30-second advertisement on television is $1000
and the estimated reach is 100,000 people. The cost of a 30-second ad
Seconds on the radio is $500 and the estimated reach is 50,000 people.
The company wants to reach a total of 200,000 people with its advertisements. Formulate a
linear programming model to determine how many ads should be placed
company in each medium to minimize the total cost of advertising.