  A concert promoter wants to book a rock group for a stadium concert. A ticket for admission to the stadium playing field will cost \$125, and a ticket.

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 A concert promoter wants to book a rock group for a stadium concert. A ticket for admission to the stadium playing field will cost \$125, and a ticket for a seat in the stands will cost \$175. The group wants to be guaranteed total ticket sales of at least \$700,000. How many tickets of each type must be sold to satisfy the groups guarantee? Express the answer as a linear inequality and draw its graph.

 A manufacturer of lightweight mountain tents makes a standard model and an expedition model. Each standard tent requires 1 labor- hour from the cutting department and 3 labor- hours from the assembly department. Each expedition tent requires 2 labor-hours from the cutting department and 4 labor-hours from the assembly department. The maximum labor-hours available per day in the cutting and assembly departments are 32 and 84, respectively.

 If the company makes a profit of \$50 on each standard tent and \$80 on each expedition tent, how many tents of each type should be manufactured each day to maximize the total daily profit (assuming that all tents can be sold)?

Decision variables x, y Objective function the profit P Constraints Cutting department constraint Assembly department constraint

 Cutting dept. constraint daily cutting time + daily cutting time ≤ max. labor hrs for x tents for y tents available per day  Assembly dept. constraint daily assembly time + daily assembly time ≤ max. labor hrs for x tents for y tents available per day  Non-negative constraints

 Mathematical model

1. Graph the feasible region. 2. Find the coordinates of each corner point. 3. Compare the values of the objective function at corner points. 4. Determine the optimal solution.

 If the optimal value of the objective function in a linear programming problem exists, then that value must occur at one (or more) of the corner points of the feasible region.

1. Select basic variables 2. Set all other variables (nonbasic variables) equal to 0 3. Solve the system : Basic solutions, basic feasible solutions

 If the optimal value of the objective function in a linear programming problem exists, then that value must occur at one (or more) of the basic feasible solutions.

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