A dress maker sells three different styles of blouses, including a Nigerian mode

Question

A dress maker sells three different styles of blouses, including a Nigerian model, a Brazilian model, and a Caribbean model. Each model produced must go through three departments: cutting, sewing, and assembly. The table below contains all relevant information concerning production times (hours per blouse), available capacity in each department per day, cost ($ per blouse and selling price per blouse). The owner has an obligation to deliver a minimum of 60 blouses in each style to a department store daily. In any case, the combined number of Nigerian style blouses and Brazilian style blouses cannot exceed 180 per day. The dress maker would like to determine the product mix that maximizes his daily profit. Formulate the problem as a linear program.

Blouse Style Cutting (hours) Sewing (hours) Assembly (hours) cost/unit Price/unit Nigerian Model 2.50 1.25 0.85 44 122 Brazilian Model 2.25 1.00 0.75 37 102 Caribbean Model 3.00 1.50 0.75 41 113 Hours Available 1360 700 430

Explanation / Answer

LP mode is as follows:

Decision variables:

Let

N = number of Nigerian models to be produced per day

B = number of Brazilian models to be produced per day

C = number of Caribbean models to be produced per day

Objective: Max (122-44)N + (102-37)B + (113-41)C

s.t.

2.5N + 2.25B + 3C <= 1360

1.25N + 1B + 1.5C <= 700

0.85N + 0.75B + 0.75C <= 430

N + B <= 180

N, B, C >= 60 (this also acts as non-negativity constraint)

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