Answer:
Solution is:
z  (max) = 687.5
x₁   =  0
x₂   = 16
x₃   = 21 
Step-by-step explanation:
From the problem statement we have:
Resources:      machine time ( 183 h)      labor (250  h)   steel  185 (pounds)
Unit 
Spoons                          4                                     4                          3
forks                               4                                     9                          2
knives5                          5                                     5                          4
Profit $                           9                                    20                       17.5
Objective function z =  9*x₁  +  20*x₂  + 17.5 *x₃   to maximize
Subject to:
Availability of machine time  :  183 h
4*x₁  +  4*x₂ +   5*x₃ ≤  183
Availability of labor  :  250 h
4*x₁  +  9*x₂  +  5*x₃  ≤  250
Availability of steel  :  185 pounds
3*x₁  +  2*x₂  +  4*x₃  ≤  185
Requirement:
x₂ ≥ 16
General constraints:
x₁  ≥ 0             x₃      ≥  0 all integers
After 6 iteration the solution using AtomZmath on-line solver
z  (max) = 687.5
x₁   =  0
x₂   = 16
x₃   = 21 
Resources used:
Machine time: 16* 4 + 21*5  =  64  +  105  = 169
remains   183 - 169  = 14 h
Labor:  16*9  +  21* 5  =  144  +  105  =  249
remains   250 -  249  =  1 h
Steel :  16*2  +  21*4  =  32  + 84  =  116
remains   185  -  116  = 69 pounds.
If it is decided that 20 units of forks are to be made then
we will need   4*4 = 16   h of machine time
                          9*4 =  36 h  of labor
                          2*4 = 8 pounds of steel
We can get that from abandom to make one unit of x₃ ??
No because as we said we need 36 hours  of  labor ( we still have 1 we need 35 more hours ) if we make 20 x₃ insted of 21 we get only 5 hours.
z we got is maximum