Question

1) Baltimore Furniture Inc. owns two factories, each of which produces three types of tables – the deluxe, medium and the standard. The company has a contract to supply tables to a newly built hotel in downtown Washington DC comprising of at least 12 deluxe tables, 8 medium tables and 24 standard tables. Each factory produces a certain number of tables during each hour it operates. Factory 1 produces 6 deluxe tables and 2 medium tables. Factory 2 produces 2 deluxe tables, 2 medium tables and 12 standard tables. It costs Baltimore Inc. $150 per hour to produce each table in factory 1 and it costs $120 per hour to produce each table from factory 2. The Company wants to determine the number of hours it needs to operate each factory so that it could meet up with its contract at the lowest cost. Hints: You are required to minimize cost assuming that factory 1 = X and factory 2 = Y.

a. Formulate a linear programming model for this problem. (15 points)

b. Represent this problem on a graph using the attached graph paper. Show the feasible region. (10 points)

c. Solve this model by using graphical analysis showing the optimal solution and the rest of the corner points as well as the costs.

Answer 1

Answer:

Here we have given that,

Deluxe. Medium. Standerd

Factory1 (x) 6. 2. 0

Factory2(y) 2. 2. 12

Total. 12. 8. 24

Then LPP for minimising the cost can be written as,

Minimise(z)=150x+120y

Subject to the constraints,

Deluxe table:

6X + 2Y ≥ 12

Medium table

2X + 2Y ≥ 8

Standard table

12Y ≥ 24

Graphical representation:

(c)

We got two points from the graph for feasible solution .i.e (1,3) and (2,2)

Cost is minimum at (1,3)

X = 1

Y = 3

For cost minimization factory 1 should be operated for 1hour and factory 2 for 3hour

Minimum cost of operation

Z = 150x1 + 120x3

Z = 150 + 360 = $510

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