Problems 173The times available on machinesA 1 andA 2 per day are 1200 and 1000 minutes, respec-
tively. The profits per unit ofB 1 , B 2 , andB 3 are $4, $2, and $3, respectively. The
maximum number of units the company can sell are 500, 400, and 600 forB 1 , B 2 , and
B 3 , respectively. Formulate and solve the problem for maximizing the profit.
3.94 Two types of printed circuit boardsAandBare produced in a computer manufacturing
company. The component placement time, soldering time, and inspection time required
in producing each unit ofAandBare given below:Time required per unit (min) for:
Circuit board Component placement Soldering Inspection
A 16 10 4
B 10 12 8If the amounts of time available per day for component placement, soldering, and inspec-
tion are 1500, 1000, and 500 person-minutes, respectively, determine the number of units
ofAandBto be produced for maximizing the production. If each unit ofAandB
contributes a profit of $10 and $15, respectively, determine the number of units ofA
andBto be produced for maximizing the profit.
3.95 A paper mill produces paper rolls in two standard widths; one with width 20 in. and
the other with width 50 in. It is desired to produce new rolls with different widths as
indicated below:Width (in.) Number of rolls required
40 150
30 200
15 50
6 100The new rolls are to be produced by cutting the rolls of standard widths to minimize
the trim loss. Formulate the problem as an LP problem.
3.96 A manufacturer produces two types of machine parts,P 1 andP 2 , using lathes and
milling machines. The machining times required by each part on the lathe and the
milling machine and the profit per unit of each part are given below:Machine time (hr) required by
each unit on:
Machine part Lathe Milling machine Cost per unit
P 1 5 2 $200
P 2 4 4 $300If the total machining times available in a week are 500 hours on lathes and 400 hours
on milling machines, determine the number of units ofP 1 andP 2 to be produced per
week to maximize the profit.