Maximize the profit:

Consider “A” be the number of assembled units for product “A” and “B” be the number of assembled units for product “B”.

Consider “A_s” be the number of sold units of product “A” and “B_s” be the number of sold units of product “B”.

Consider “A_B” be the number of units of “A” that were used to produce type “B” products.

Consider “R_p” be the units of raw material produced and “R_b” be the units of raw materials bought.

The selling cost of type “A” product is $11 and the same for type “B” product is $23.

Then, the selling cost of “A_s” and “B_s” units are given by Z = 11As+23Bs.

The per unit cost of raw material is $5.

Then, the total cost for the raw material is “5R_b”.

The net profit of the problem is constructed as follows:

Z = 11As+23Bs−5Rb

Since the profit function needs to be maximized, the objective function of the problem is shown as follows:

Maximize, Z = 11As+23Bs−5Rb

Constraint 1:

A unit of type “A” product requires 2 hours on assembly line 1.

Also, one unit of type “B” requires 1 unit of type “A” which requires 2 hours on assembly line 1. Then “R_p” units of type “B” requires “3R_p” hours on assembly line 1.

Then the total hours required for assembly line 1 is “2A + 2R_p”

It is given that at most, 1300 hours of time are available for line 1

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Solution Summary: The objective function of the problem is shown as follows: Maximize the profit.

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