QUESTION 1 Use the following scenario and data for questions 1 to 10 Grolf Kitch

Question

QUESTION 1 Use the following scenario and data for questions 1 to 10 Grolf Kitchen, L.L.C makes two tynes of herhoque grilk The availahilty of throe scrce reoaoes limits the production of the grills The prot conribution resource woge per unit of each grill and availsblity of the resouroes sre givn in the Sollowing lable Unt Gnll2 Rescurce Gnll Availabal 180 420 t Contnbution The decision variables used in the liner programming model are .,-number of unix of grill l to prodaxg x,-number of unts of gnil 2 to produce model and the graghic The lince programming solution are gien in the Tollowi ing 2,+3, s 180 +2x,S 200 7s, +6x, 420 100 90 80 Ferable region 30 Optimal solution 36 29) 50 30 20 10 0 20 6090100 10

Explanation / Answer

The objective function for the above linear programming problem is given by the equation-

Z = 15 x1 + 12 x2

The coefficient of x1 is c1, i.e. 15.

The coefficient of x2 is c2, i.e. 12.

In the above graph, x1 is taken on the x-axis and x2 is taken on the y-axis. Hence the slope of the objective function can be found out by comparing it to the equation y = m * x + c

where y represents the y-axis value, x represents the x-axis value, m represents the slope of the line and c represents the intercept on the y-axis.

Now,

Rearranging our primary objective function, we get,

x2 = -(15/12) x1 + (Z/12)

By comparing this above equation with the equation y = m * x + c, we see that,

m = -(15/12) i.e. - (c1/c2)

Hence the correct answer is option C.

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