Each coffee table produced by Home Woods nets the firm a profit of $15. Each bookcase...
Each coffee table produced by Home Woods nets the firm a profit of $15. Each bookcase yields a $20 profit. Home Wood’s firm is small and its resources limited. During any given production period (of 1 week), 20 gallons of varnish and 15 lengths of high quality redwood are available. Each coffee table requires approximately 2 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood. Assume minimum 4 coffee table and 5 bookcases should be produced per week.
Formulate this manufacturing problem and then find the optimal solution.
Homework Answers
Since the objective is to maximise the profit, the objective function is
Max (15X+20Y)
where X and Y are the number of coffee table and bookcase manufactured respectively.
Constraints
2X+y<=20
X+2y<=15
X=>4
Y=>5
The points of optimality are ( 4,5.5)(5,5) (4,12) and (7.5,5)
Value of objective function
at (4,5) = 160
at(5,5) =175
at(4,12) = 300
at(7,5) =205
The most optimal value is X=4, Y=12 with output of 300
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