A bicycle manufacturer builds one three and tenspeed models

A bicycle manufacturer builds one-, three- and ten-speed models. The bicycles need both aluminum and steel. The company has available 51,325 units of steel and 63,480 units of aluminum. The one-, three-, and ten-speed models need, respectively, 10, 12 and 15 units of steel and 24, 12, and 30 units of aluminum. How many of each type of bicycle should be made in order to maximize profit if the company makes $6 per one-speed bike, $12 per three-speed, and $30 per ten-speed. What is the maximum possible profit? Type the number of each type of bicycle that should be made. One-speed: Three-speed: Ten-speed: A bicycle manufacturer builds one-, three- and ten-speed models. The bicycles need both aluminum and steel. The company has available 33,465 units of steel and 57,100 units of aluminum. The one-, three-, and ten-speed models need, respectively, 9, 12 and 15 units of steel and 20, 15, and 25 units of aluminum. How many of each type of bicycle should be made in order to maximize profit if the company makes $3 per one-speed bike, $4 per three-speed, and $10 per ten-speed. What is the maximum possible profit? Type the number of each type of bicycle that should be made. One-speed: Three-speed: Ten-speed: A cat breeder has the Yellowing amounts of cat food: 90 units of tuna, 80 units of liver, and 60 units of chicken. To raise a Siamese cat, the breeder must use 2 units of tuna, 2 of liver, and 3 of chicken, while raising a Persian cat requires 2, 2 and 3 units respectively per day. If a Siamese cat sells for $ 14, and a Persian cat sells for $16, how many of each should be raised in order to obtain maximum gross income? Set up the initial simplex tableau. Set up the initial simplex tableau for the problem. Let x_1 be the number of Siamese cats, and let x_2 be the number of Persian cats. Begin by filling in missing terms for constraints. 2x_1 + 2x_2 lessthanorequalto is the constraint on tuna consumption. 2x_1 + 2x_2 lessthanorequalto is the constraint on liver consumption. 3x_1 + 3x_2 lessthanorequalto is the constraint on chicken consumption.

Solution

Let x nos 1speed model , y nos. 2speed model and z 3speed model.

Al : 1speed model ---9 units , y nos. 2speed model----12 units and z 3speed model----15 units.

9x + 12y +15z <= 33465

Steel : 1speed model ---10 units , y nos. 2speed model----20 units and z 3speed model----25 units.

10x +20y +25z <= 57100

Objective function : P = 3x +4y +10z

Use the simplex method:

Tableau #1
x y z s1 s2 p   
9 12 15 1 0 0 33465
10 20 25 0 1 0 57100
-3 -4 -10 0 0 1 0

Tableau #2
x y z s1 s2 p   
0.6 0.8 1 0.0666667 0 0 2231
-5 0 0 -1.66667 1 0 1325
3 4 0 0.666667 0 1 22310   

The optimal solution : p = 22310;

1- speed model x = 0, 2- speed model y = 0, 3- speed model z = 2231