MATLAB: How to use linprog solver for some values of variables needs to have equal value

linprog constant variables

How i could use linprog to solve this problem. My objective and constraint have this form.
Objective Pa – -> max
A x + B y = a
C x + Pa*D <= b
and Pa >=0
I don't want to use nonlinear constraint or need to know any other function (without using nonlinear constraint) to get the optimized value for Pa 
A = [-1  1  0	 0  0
      1 -2  1	 0  0
      0  1 -2	 1  0
      0  0  1 -2  1
      0  0  0	 1 -1 ] 
B = [-1 0; 0 0; 0 0; 0 0; 0 -1]'
a = [0 0 0 0 0]'
C = [ 1  0  0	 0  0
      0  1  0	 0  0
      0  0  1	 0  0
      0  0  0	 1  0
      0  0  0	 0  1
     -1  0  0	 0  0
      0 -1  0	 0  0
      0  0 -1	 0  0
      0  0  0	-1  0
      0  0  0  0 -1]
 D = [4.50, 0.90, 2.70, 0.90, 4.50, 4.50, 0.90, 2.70, 0.90, 4.50]'
 b = [3.00, 3.00, 3.00, 3.00, 3.00  6.00, 6.00, 6.00, 6.00, 6.00]'

Best Answer

A = [-1  1  0	 0  0
      1 -2  1	 0  0
      0  1 -2	 1  0
      0  0  1 -2  1
      0  0  0	 1 -1 ]; 
B = [-1 0 0 0 0
      0 0 0 0 0
      0 0 0 0 0
      0 0 0 0 0
      0 0 0 0 -1];
a = [0 0 0 0 0].';
C = [ 1  0  0	 0  0
      0  1  0	 0  0
      0  0  1	 0  0
      0  0  0	 1  0
      0  0  0	 0  1
     -1  0  0	 0  0
      0 -1  0	 0  0
      0  0 -1	 0  0
      0  0  0	-1  0
      0  0  0  0 -1];
D = [4.50, 0.90, 2.70, 0.90, 4.50, 4.50, 0.90, 2.70, 0.90, 4.50].';
b = [3.00, 3.00, 3.00, 3.00, 3.00  6.00, 6.00, 6.00, 6.00, 6.00].';
Aeq=[A, B, zeros(5,1)] 
beq=a
Aineq=[C,zeros(10,5), D]
bineq=b
f=[zeros(10,1);-1]
lb=[-Inf*ones(10,1);0]
ub=[Inf*ones(11,1)]
x=linprog(f,Aineq,bineq,Aeq,beq,lb,ub)
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