Problem 222a Formulate An LP Model

Problem 2.22:
a. Formulate an LP model for this problem
X1 = quantity of ornate, decorative wood frame doors produced
X2 = quantity of windows produced
Max Total Profit: 500X1+400X2
X1+0.5*X2≤40
0.5*X1+0.75*X2≤40
0.5 X1+X2≤60
X1, X2≥0
b. Sketch the feasible region
Please refer to the graph below

c. What is the optimal solution
After calculations using solver in excel, we figure out that the max total profit available is $26,000.00, when produce a mix of 20 units of doors and 40 units of windows.

Problem 3.21:
a. Formulate an LP model for this problem
X1 = quantity of HyperLink
X2 = quantity of FastLink
X3 = quantity of SpeedLink
X4 = quantity of MicroLink
X5 = quantity of EtherLink
Max Total profit: 53X1+48X2+33X3+32X4+38X5
20*X1+15*X2+10*X3+8*X4+5*X5≤80000
28*X1+24*X2+18*X3+12*X4+16*X5≤100000
8*X1+8*X2+4*X3+4*X4+6*X5≤30000
0.75*X1+0.6*X2+0.5*X3+0.65*X4+X5≤5000
X1, X2, X3, X4, X5≥500
X2≥2*X1
b. What is the optimal solution
After calculations using solver in excel, we figure out that the max total profit available is $215,000.00, when produce a mix of 500 units of HyperLink, 1000 units of FastLink, 1500 units of SpeedLink, 2250 units of MicroLink and 500 units of EtherLink.
c. Could Valu-Com make more money if it schedules assembly workers to work overtime?
No, because for this optimal solution, the Valu-Com Electronics has already run out of Resistors for production. Even if it schedules assembly workers to work overtime, they cannot make any more productions to make more money.