Gulf, Inc manufactures golf equipment and supplies. The company wants to produce
ID: 393022 • Letter: G
Question
Gulf, Inc manufactures golf equipment and supplies. The company wants to produce standard and deluxe golf bags. Gulf profits $12 for each standard bag produced and sold, and $9 for each bag deluxe bag produced and sold. Gulf has the following operations for the production of the bags: (1) Cutting and dyeing the material (2) Sewing (3) Finishing. Required production time and total available time in each department are shown in the table below.
(a) Define decision variables of the LP model as carefully as you can.
(b) Write down the objective function for this profit maximizing company.
(c) Write all constraints of the LP problem.
(d) Assume the optimal numbers of Standard and Deluxe golf bags to be produced are calculated as 540 and 250. What is the optimal objective value?
Department Standard Production time (hours) Deluxe Production time (hours) Hours available Cutting and dyeing 7/10 1 630 Sewing 1/2 5/6 600 Finishing 1 2/3 708Explanation / Answer
a) Decision variables -
S = Number of Standard golf bags
D = Number of Deluxe golf bags
b) The objective function is -
Maximize Profit Z = 12S+9D
c) Constraints of the model -
(7/10)*S+D <= 630 => 7S+10D <= 6300 --> Cutting and dyeing hours
(1/2)*S+(5/6)*D <= 600 --> 3S+5D <= 3600 --> Sewing hours
S+(2/3)*D <= 708 --> 3S+2D <= 2124 --> Finishing hours
S,D >= 0 --> Non-negativity constraints
d) Optimal objective value for S = 540 and D = 250
Z = (12*540)+(9*250) = 8730 $
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.