Solve the linear programming problem by the simplex method.
Maximize P = x+ 2y-z

subject to 2x + y + z ≤ 8
            4x + 2y + 3z ≤ 16
            2x + 5y + 5z ≤ 32
               x ≥, y ≥ o, z ≥ 0
The maximum is P =             at (x, y, z) = ( ).

Solve the linear programming problem by the simplex method. (There may be more than one correct answer.)
Maximize P = 3x + 3y + 4z
subject to x + y + 3z ≤ 15
            4x + 4y + 3z ≤ 215
               x ≥ o, y ≥ o, z ≥ o
The maximum is P = 45 at (x,y,z) = ( ).

Solve the linear programming problem by the simplex method.
Maximize    P =x+4y-2z
subject to       3x + y - z ≤52
                     2x + y - z ≤ 26
                     - x + y + z ≤ 52
                     x ≥ o, y ≥ o, z ≥ 0
The maximum is P =             at (x, y, z) = ( ).

Boise Lumber has decided to enter the lucrative prefabricated housing business. Initially, it plans to offer three models: standard, deluxe, and luxury. Each house is prefabricated and partially assembled in the factory, and the final assembly is completed on site. The dollar amount of building material required, the amount of labor required in the factory for prefabrication and partial assembly, the amount of on-site labor required, and the profit per unit are as follows.
                        Standard Model Deluxe Model    Luxury Model
Material                $6,000                $8,000             $10,000
Factory Labor (hr)    240                      220                   200
On-Site Labor (hr)    180                      210                   300
Profit                      $3,400                $4,000                $5,000

For the first year's production, a sum of $8,200,000 is budgeted for the building material; the number of labor-hours available for work in the factory (for prefabrication and partial assembly) is not to exceed 212,000 hr; and the amount of labor for on-site work is to be less than or equal to 231,000 labor-hours. Determine how many houses of each type Boise should produce to maximize its profit from this new venture. (Market research has confirmed that there should be no problems with sales.)
standard model       houses
deluxe model          houses
luxury model          houses

CalJuice Company has decided to introduce three fruit juices made from blending two or more concentrates. These juices will be packaged in 2-qt (64-oz) cartons. One carton of pineapple orange juice requires 8 OZ each of pineapple and orange juice concentrates. One carton of orange-banana juice requires 12 OZ of orange juice concentrate and 4 oz of banana pulp concentrate. Finally, one carton of pineapple-orange-banana juice requires 4 OZ of pineapple juice concentrate, 8 OZ of orange juice concentrate, and 4 OZ of banana pulp concentrate. The company has decided to allot 16,000 oz of pineapple juice concentrate, 24,000 OZ of orange juice concentrate, and 5000 OZ of banana pulp concentrate for the initial production run. The company also stipulated that the production of pineapple- orange-banana juice should not exceed 620 cartons. Its profit on one carton of pineapple-orange juice is $1.00, its profit on one carton of orange-banana juice is $0.80, and its profit on one carton of
pineapple-orange-banana juice is $0.90. To realize a maximum profit, how many cartons of each blend should the company produce?
pineapple-orange juice             cartons
orange-banana juice                   cartons
pineapple-orange-banana juice cartons

What is the largest profit it can realize?
$

Are there any concentrates left over? (If so, enter the amount remaining. If not, enter o.) pineapple concentrate       OZ
orange concentrate          OZ
banana pulp concentrate    OZ

Solve the linear programming problem by the simplex method. Maximi...