Question

Consider the following case to form singular matrix with different combination of input pertaining to Car manufacturing Company, Juice

Company and Chips Company. For every case make a 3*3 matrix.

Case I: Steel, Rubber, Glass

Case II: Fruit pulp, Sugar, Preservatives

Case III: Potatoes, Spices, Corn Starch​

Answer 1

Answer:

Let factories I and II should be operated for x and y number of days respectively. Then the problem can be formulated as in L.P.P. as:

Minimise Z=12000x+15000y

Subject to constraints

$50x+40y≥6400 i.e., 5x+4y≥640</p><p> \\ 50x+20y≥4000 i.e., 5x+2y≥400</p><p> \\ 30x+40y≥4800 i.e., 3x+4y≥480</p><p> \\ x≥0,y≥0$

We draw the lines

$5x+4y≥640, \\ 5x+2y≥400, \\ 3x+4y≥480$

and obtain the feasible region (unbounded and convex) shown shaded in the adjoining figure. the corner points are

$A(0,200),B(32,120),C(80,60) \\ and D(160,0)$

The values of Z at these points are 3000000,2184000,1860000 and 1920000 respectively. As the feasible region is unbounded, we draw the graph of the half plane.

$12000x+15000y<1860000$

i.e.,

$12x+15y<1860$

and note that there is no point common with the feasible region, therefore Z has minimum and minimum value is Rs. 1860000.

It occurs at the point (80,60) i.e., Factory I should be operated for 80 days and factory II should be operated for 60 days to minimise the cost.

Step-by-step explanation:

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