Finer Furniture produces three types of wooden furniture – benches, tables, and
ID: 2936033 • Letter: F
Question
Finer Furniture produces three types of wooden furniture – benches, tables, and chairs. The production of each of these involves both a carpentry process and a finishing process. The time required in each of these as well as lumber requirements for each product are given below. For example, it takes 3 carpentry hours, 2 finishing hours, and 10 feet of lumber to produce one bench. The profit per unit is also given in the table.
Benches
Tables
Chairs
Amount available per month
Carpentry hours
3 hr.
6 hr.
5 hr.
1800
Finishing hours
2 hr.
5 hr.
4 hr.
1200
Lumber (Feet)
10 ft.
30 ft.
15 ft.
4800
Profit
$40
$60
$70
The company wishes to get the maximum profit possible, and a linear program was developed for this purpose. The variables were defined as:
B = number of benches produced each month; T = number of tables produced each month
C = number of chairs produced each month
The linear program is:
Maximize Profit = 40B + 60T + 70C
Subject to:
3B + 6T + 5C < 1800
2B + 5T + 4C < 1200
10B + 30T + 15C < 4800
B, T, C > 0
a. (2 points) Suppose the company produced 80 benches, 100 tables, and 80 chairs. Find the total profit and the amount of each resource used. Put your answers on the answer sheet.
b. (6 points) Find the optimal solution, and put the answers in the table on the answer sheet.
c. (2 points) What is the dual price (value) for the finishing hours (constraint #2)? Now add 1 hour to the total finishing hours and solve the problem again. What is the maximum total profit?
Answer Sheet:
Profit
Benches produced
Tables produced
Chairs produced
Carpentry hours used
Finishing hours used
Feet of lumber used
a.
b.
Dual value =
Total profit =
c.
Is the solution in part a feasible (yes or no)?
Benches
Tables
Chairs
Amount available per month
Carpentry hours
3 hr.
6 hr.
5 hr.
1800
Finishing hours
2 hr.
5 hr.
4 hr.
1200
Lumber (Feet)
10 ft.
30 ft.
15 ft.
4800
Profit
$40
$60
$70
Explanation / Answer
The total furniture hours was 1199 when the B,T,C are 115,1,241
Change the constraint to f10 <=1201 and solve again.
But when we increased the maximum furniture hours as 1201 available, the B,T,C are114,1 and 242
and the total furniture hours used was 1201. It increased the profit to 21520
c)
solutiof of 80B, 100T and 80B is not possible as it is violating the constraint of lumber.
Total available is 4800, but this solution is taking it to 5000 ft.
Hence not possible.
Profit Benches produced Tables produced Chairs produced Carpentry hours used Finishing hours used Feet of lumber used a. 14800 80 100 80 1240 980 5000 b. 21350 115 1 241 1556 1199 4795 Dual value =1199 Total profit =21560 c. Is the solution in part a feasible (yes or no)? NORelated Questions
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