Problem 1: Morzda is considering expanding their production capabilities in a factory. The factory
currently makes three types of cars: 3, 6, and X5. Each car has a requirement of steel, labor, and
expected profit given in the table below:
Resource
3
6
X5
Steel
1.5 tons
2 tons
3 tons
Labor
30 hours
28 hours
40 hours
Profit
$2000
$2500
$3500
Morzda currently has 6000 tons of steel and 60,000 hours of labor at the plant. Lastly, Morzda does
not consider it economically viable to produce X5 unless at least 700 of them are produced.
a. Formulate an integer program that would allow Morzda to maximize their profit.
b. The company has the option to hire part time help. In total, they could obtain 5000 new
hours of labor for the price of $50,000. Modify your model from part (a) to determine if they
should make this change.
c. Morzda is considering using lightweight materials to reduce the amount of steel used. To
reconfigure their machines, it would cost $25,000; but would reduce the amount of steel needed
for a 3, 6, and X5 to be 1.25 tons, 1.8 tons, and 2.85 tons, respectively. Again, modify your
model from part (a) to determine if they should make this change.
