Write the objective function and the inequalities that describe the constraints in each problem. Graph the feasibility region, showing the corner points. Then find the maximum or minimum value of the objective function. Band trips A high school band trip will require renting buses and trucks to transport no fewer than 100 students and 18 or more large instruments. Each bus can accommodate 40 students plus three large instruments; it costs $\$ 350$ to rent. Each truck can accommodate 10 students plus 6 large instruments and costs $\$ 200$ to rent. How many of each type of vehicle should be rented for the cost to be minimum? Find the minimum cost.
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An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. Objective Function z = 7x - 16y Constraints 0 ≤ x ≤ 5 0 ≤ y ≤ 8 4x + 5y ≤ 30 4x + 3y ≤ 20 maximum: 35; at (5, 0) maximum: -71.25; at (1.25, 5) maximum: 0; at (0, 0) maximum: -96; at (0, 6)
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An objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of $x$ and $y$ for which the maximum occurs. Objective Function Constraints $$ \begin{aligned} &z=10 x+12 y\\ &\left\{\begin{array}{l} {x \geq 0, y \geq 0} \\ {x+y \leq 7} \\ {2 x+y \leq 10} \\ {2 x+3 y \leq 18} \end{array}\right. \end{aligned} $$
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