1 Marks

Question 1: Formulate and solve the following problem

A manufacturer produces 2 types of Strawberry A and B yogurts from Strawberry, Milk and Sugar. Each yoghurt must respect the following proportions of raw materials.

Type

A

B

Strawberry

2

1

Milk

1

2

Sugar

0

1

800 kg of Strawberry, 700 kg of Milk and 300 kg of sugar are available.

The sale of 1 kg of yogurts A and B respectively yields $4 and $5.

The manufacturer seeks to Maximize profit.

1)Formulate the linear program by answering the following questions (3.5 points):

What are the decision variables?

...............................................................................................................................................................................................................................

What is the objective function?

.................................................................................................................

What are the constraints of the problem?

.............................................................................................................................................................................................................................................................................................................................................

2)Solve the above problem graphically

Step 1: sketch the constraints

........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

Step 2: Identify the Feasible Region On the graph

.................................................................................................................

Step 3: sketch the Objective Function

)

Step 4: Determine the Optimal solution (O*) of the problem (1 point) then interpret the optimal Profit (Z*)

1

Question 2: write true or False

1.Iconic models: are physical in form, but do not physically resemble the object being modeled

2.A mathematical model is said stochastic if one of uncontrollable inputs are subject to variation.

3.A company has seven permanent employees whose monthly salaries are$ 100 000. Does this amount represent the total variable costs of this company?

4.To calculate the Break-even Point, we only need to determine the expression of Total Revenue.

5.Objective function is the restriction or limitation on the decision variables.

6.Linear functions are functions in which each variable appears in a separate term raised to the first power and is multiplied by a constant (which could be 0).

1

Question 3: write true or False

1.Consider that: Maxz = 4x + 2y and its graph is the following

What is the optimal solution?

b. Infeasible Region

c. Unbounded Feasible Region

d. alternative solutions

2.Consider that: and its graph is the following:

What is the optimal solution?

b. Infeasible Region

c. Unbounded Feasible Region

d. alternative solutions

3.Consider that:Maxz = 2x + 2y and its graph is the following:

What is the optimal solution?

b. Infeasible Region

c. Unbounded Feasible Region

d. alternative solutions

4.The linear model consists of A set of decision variables, a set of constraints and:

a.An objective function

b.b. Two objective functions

c. Three objective functions

d.Many objective functions

2

Question 4: BREAK-EVEN POINT--------

Exercise 1:Peter Garcia Meza is considering buying a company if it will break even or earn net income on revenues of $80,000 per month. The company that Peter is considering sells each unit it produces for $5. Use the following cost data to compute the variable cost per unit and the fixed cost for the period. Calculate the break-even point in sales dollars. Should Peter buy this company?

Volume (units)

Cost

8,000

$70,000

68,000

190,000

2.The Break-even point graph is the following

Line 1 represents:

a.Total revenue line

b.Fixed cost line

c.Total variable costs line

3.The Break-even point graph is the following

The value of fixed cost (FC) is

a.0

b.50 000

b.100 000

c.

Exercise 1:Peter Garcia Meza is considering buying a company if it will break even or earn net income on revenues of $80,000 per month. The company that Peter is considering sells each unit it produces for $5. Use the following cost data to compute the variable cost per unit and the fixed cost for the period. Calculate the break-even point in sales dollars. Should Peter buy this company?

Volume (units)

Cost

8,000

$70,000

68,000

190,000