Jack can produce red and green chilies T-shirts on six different machines. The following table summarizes the manufacturing costs associated with producing T-shirts on each machine along with the available capacity on each machine. If Jack received an order of 1800 T-shirts, how should Jack schedule these machines, i.e. which machine produces how many T-shirts to minimize the total cost?
Machine Fixed Cost Variable Cost Capacity
1 $1000 $21 500
2 $950 $23 600
3 $875 $25 750
4 $850 $24 400
5 $800 $20 600
6 $700 $26 800
Formulate an IP to solve this problem. I suggest you write out the complete formulation before answer the multiple-choice questions.
Decision Variables:
Xi: number of T-shirts produced on the machine i. i=1-6.
Parameters:
FCi: Fixed cost of machine i, i=1-6.
VCi: Variable cost of machine i, i=1-6.
CAPi: Capacity of machine i, i=1-6.
Question 1:
What should be the objective function?
a.) Max 21X1+23X2+25X3+24X4+20X5+26X6
b.) Max
Where Yi =1 if Xi positive; 0 otherwise
c.) Min 21X1+23X2+25X3+24X4+20X5+26X6
d.) Min
Where Yi =1 if Xi positive; 0 otherwise
Question 2:
Let Yi=1 if Xi positive; 0 otherwise, i=1-6.
Which of the following statement regarding the production setup constraint is not true?
a.) We use Xi-MiYi<=0 where Mi is large enough number to ensure when Xi is positive, Yi is 1.
b.) We can not use Xi-XiYi as the production setup constraint because it is nonlinear.
c.) The decision variable Yi represents whether or not to use machine i.
d.) As long as M2 is larger than 400, it is large enough for the production setup constraint X2-M2Y2<=0
Question 3:
Which of the following constraint is not part of the IP formulation?
a.) X3-750Y3<=0
b.) X2<=600
c.)
6
ΣΧis 1800
1=1
1
d.) Yi binary
Question 4:
What are the optimal solutions and minimized cost?
a.) X1=400, X2=600, X5=700, X6=100, and the minimized total cost is 42250
b.) X2=600, X3=500, X5=600, X6=100, and the minimized total cost is 44225.
c.) X1=500, X2=600, X5=600, X6=200, and the minimized total cost is 42350.
d.) X1=500, X2=600, X5=600, X6=100, and the minimized total cost is 42350.