Optimum Design
185
PROBLEM 3.8
A casting company wishes to know the production of products (P~, P2, P3,
P4, Ps, P6) in Table Problem 3.8 which will give a maximum profit. The
operations are shown below.
Table Problem 3.8
Available
Operating
Product
Operation
Time/Wk
Cost
Time/Unit(min.)
P~
P2
P3 P4 P5 P6
M~ casting
2200 min
$0.15/min
8
3
4
5
6
2
M2 deburring
2400 min
$0.08/min
4
4
6
2
3
2
M3 drilling
2400 min
$0.17/min
0
1
2
8
4
3
M4 tapping
400 min
$0.09/min
4
6
2
0
0
0
M5 drilling
400 min
$0.012/min 1
5
2
0
0
0
Material cost
0.80 0.65 0.30 0.40 0.45 1.00
Selling price/unit
7.00 5.50 4.50 5.50 4.30 4.00
Solve for P~-P6 to maximize profit
PROBLEM 3.9
A steam plant [3.16] has two boilers which it normally operates. Both are
equipped to burn either coal, oil, or gas according to the following
efficiencies:
Coal
Oil
Gas
Boiler 1
0.80
0.82
0.84
Boiler 2
0.60
0.65
0.76
Total steam supply required of the two boilers is 150 heat units/day. Maximum output Boiler 1 is 100 units/day and of Boiler 2 is 90 units/day.
A contract requires 120 units of gas/day to be purchased; maximum limit
on coal must be 150 heat units/day; and oil must be 20 heat units/day.
Coal
Oil
Gas
Fuel costs in cents/heat unit
25
27
29