Minimize C=7x+3y+4z

0≤x
0≤y
0≤z
100≤2x+3y+3z
120≤5x+2z

Answer: Minimum value of C =?

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To minimize the objective function C=7x+3y+4z subject to the given constraints, we need to apply linear programming. Here's a step-by-step approach to solve it:

1. Begin by identifying the decision variables. In this case, the variables are x, y, and z.

2. Formulate the objective function. The objective function is to minimize C=7x+3y+4z.

3. Define the constraints. Based on the given information, the constraints are as follows:
- Non-negativity: 0 ≤ x, 0 ≤ y, 0 ≤ z
- Constraint 1: 100 ≤ 2x+3y+3z
- Constraint 2: 120 ≤ 5x+2z

4. Convert the constraints to the same format. Let's rewrite constraint 1 and constraint 2 to have the same variables:
- Constraint 1: -2x-3y-3z ≤ -100
- Constraint 2: -5x-2z ≤ -120

5. Set up the initial LP problem. We have:
- Objective function: Minimize C = 7x+3y+4z
- Constraints:
- 0 ≤ x
- 0 ≤ y
- 0 ≤ z
- -2x-3y-3z ≤ -100
- -5x-2z ≤ -120

6. Solve the LP problem using a linear programming solver or a graphical method to find the optimal values of x, y, and z that minimize C. The solver will provide the optimal value for C.

Note: The specific solution depends on the exact values of the coefficients in the objective function and constraints. You can use software like Excel with Solver add-in or online LP solvers to obtain the numerical values of x, y, z, and C.

Once the LP problem is solved, the minimum value of C will be the optimal value obtained from the solver.