Answer to Question #153833 in Microeconomics for Mar

Question

The manufacturer has 60 EUR at its disposal. Production resources cost X -2EUR, Y -6 EUR. The manufacturer can use combinations of the following factors to produce 200 items: 
2X, 20Y;
 6X, 10Y; 
10X, 5Y;
 15X, 4Y; 
20X, 4Y.
How many factors must be purchased for this manufacturer to reach the manufacturer's balance by producing 200 units?

Answer 1

Objective function

Maximize 2x+6y: Constraints : x+y<=60 : 2x+20y<=200 : 10x+5y<=200, and X,Y=>0

(Use any of the input combinations and equate to 200.)

Solution by either simplex method or graphically yields X and Y maximized at app. 16 and 8 respectively.

Therefore, the manufacturer must piurchase 16 units of factor X and 8 units of factor Y.

See the attached plots.