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te available for cultivating Barley requires S10 per acre for cultivation, oats

ID: 3047931 • Letter: T

Question

te available for cultivating Barley requires S10 per acre for cultivation, oats per acre for cultivation, and wheat requires $12 e cultivation. Barley requires 7 hours of laboer e or require 9 hours of labor per acre, and wheat requires Oats of labor per acre. The firm has 2100 hours of lab The profits per acre of each crop are barley $60, oats $7s able, wheat $70. How many acres of each crop shouldbeplan d maximize profit? at 22. Agricullur acre for per acre, or availab to akes chairs, sofas, and tables. The amounts of labor of trei ous types, as well as the relative availability of each type summarized by the following chart: 23. Furniture Factory Suppose that a furniture Daily Labor Available Chair Sofa Table (labor-hours 768 144 216 Carpentry 3 Finishing Upholstery 0 The profit per chair is $80, per sofa $70, and per table $120. How many pieces of each type of furniture should be manu- factured each day to maximize the profit? 24. Stereo Store A stereo store sells three brands of stereco ses tems, brands A, B, and C. It can sell a total of 100 stereo systems per month. Brands A, B, and C take up, respectively: 5, 4, and 4 cubic feet of warehouse space, and a maximum of 480 cubic feet of warehouse space is available. B, and C generate sales commissions of $40, $20, an respectively, and $3200 is available to pay the sales com sions. The profit generated from the sale of each brand i S210, and $140, respectively. How man of nnah d S30 reo sstem gh 11 rand of ste

Explanation / Answer

23)
chair -x, sofa -y , table - z
maximize p = 80x + 70y + 120z

6x + 3y + 8 z <= 768
x+y+ 2z < = 144
2x+5y <= 216

Tableau #1
x      y      z      s1     s2     s3     p           
6      3      8      1      0      0      0      768  
1      1      2      0      1      0      0      144  
2      5      0      0      0      1      0      216  
-80    -70    -120   0      0      0      1      0    

Tableau #2
x      y      z      s1     s2     s3     p           
2      -1     0      1      -4     0      0      192  
0.5    0.5    1      0      0.5    0      0      72   
2      5      0      0      0      1      0      216  
-20    -10    0      0      60     0      1      8640

Tableau #3
x      y      z      s1     s2     s3     p           
1      -0.5   0      0.5    -2     0      0      96   
0      0.75   1      -0.25 1.5    0      0      24   
0      6      0      -1     4      1      0      24   
0      -20    0      10     20     0      1      10560

Tableau #4
x         y         z         s1        s2        s3        p                 
1         0         0         0.416667 -1.66667 0.0833333 0         98      
0         0         1         -0.125    1         -0.125    0         21      
0         1         0         -0.166667 0.666667 0.166667 0         4       
0         0         0         6.66667   33.3333   3.33333   1         10640   

Optimal Solution: p = 10640; x = 98, y = 4, z = 21

Note: this can be solved using software excel, LINDO etc

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