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Published byMeredith Montgomery Modified over 6 years ago

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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.

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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.

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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)?

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

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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

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Mathematical model

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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.

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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.

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

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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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