The Janie Gioffre Drapery Company makes three types of draperies at two differen

Question

The Janie Gioffre Drapery Company makes three types of draperies at two different locations. At location I, it can make 10 pairs of deluxe drapes, 20 pairs of better drapes, and 13 pairs of standard drapes per day. At location II, it can make 20 pairs of deluxe, 50 pairs of better, and 6 pairs of standard per day. The company has orders for 3000 pairs of deluxe drapes, 6300 pairs of better drapes and 1800 pairs of standard drapes. If the daily costs are $650 per day at location I and $750 per day at location II, how many days should Janie schedule at each location in order to fill the orders at minimum cost? location I _______ days location II _______ days Find the minimum cost. $ _______

Explanation / Answer

Let us say, production is scheduled for 'x' number of days at loaction I and 'y' number of days at location II.

Accordingly the total production of number of deluxe pairs would be 10x, better pairs 20 x and standard pairs 13x at location I and total production of number of deluxe pairs would be 20y, better pairs 50 y and standard pairs 6y at location II

The combined production at two locations should be 10x +20y= 3000   (A); 20x +50y= 6300    (B): and 13x +6y= 1800 (C)

Obviously, x>= 0 and y>=0

It is required to minimise cost function C= 650x +750 y.

Solving the system of equations (A) and (B), it would be x= 240, y= 30

Solving the system of equations (B) and (C), it would be x=98, y= 87 (round figures)

Solving the system of equations (A) and (C), it would be x= 90, y= 105

For x= 240, y=30 ; C= 650*240 + 750*30 =156,000+22,500=178,500

For x= 98, y=87 ;   C= 650*98 + 750*87 =63,700+65,250=128, 950

For x= 90, y= 105; C= 650*90 + 750*105 =58,500+78,750=137, 250

Thus mimimum cost would be for x= 98 days and y = 87 days.

Thus at location I ,   98 days

             location II, 87days

Minimum cost $ 128, 950

                                                               *******

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