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Linear Programming Assignment
Terms in this set (13)
A manufacturer produces two types of bottled coffee drinks: cappuccinos and cafés au lait. Each bottle of cappuccino requires 6 ounces of coffee and 2 ounces of milk and earns a profit of $0.40. Each bottle of café au lait requires 4 ounces of coffee and 4 ounces of milk and earns a profit of $0.50. The manufacturer has 720 ounces of coffee and 400 ounces of milk available for production each day. To meet demand, the manufacturer must produce at least 80 coffee drinks each day. Let x = the number of cappuccino bottles and y = the number of café au lait bottles.
Identify the constraints on the system other than
x ≥ 0 and y ≥ 0.
Complete the objective function.
A system has the following constraints:
x + y ≥ 80
3x + 2y ≤ 360
x + 2y ≤ 200 x ≥ 0
y ≥ 0
Which graph represents the feasible region for the system?
The vertices of the feasible region represented by a system are (0, 100), (0, 80), (80, 60), (80, 0), and (120, 0).
What are the minimum and maximum values of the objective function F = 8x + 5y?
A printing company orders paper from two different suppliers. Supplier X charges $25 per case. Supplier Y charges $20 per case. The company needs to order at least 45 cases per day to meet demand and can order no more than 30 cases from Supplier X. The company needs no more than 2 times as many cases from Supplier Y as from Supplier X. Let x = the number of cases from Supplier X and y = the number of cases from Supplier Y.
Complete the constraints on the system.
y less than equal to x
x + y greater than equal to
x less than equal to
The printing company wants to minimize costs. What is the objective function?
The graph represents the feasible region for the system:
y es001-1.jpg 2x x + y es001-2.jpg 45
x es001-3.jpg 30
Minimize the objective function P = 20x + 16y.
The minimum value =
and occurs when x =
and y =
x es002-1.jpg 0, y es002-2.jpg 0, 2x + 2y es002-3.jpg 4, x + y es002-4.jpg 8
Explain the steps for maximizing the objective function P = 3x + 4y.
Graph the inequalities given by the set of constraints. Find points where the boundary lines intersect to form a polygon. Substitute the coordinates of each point into the objective function and find the one that results in the largest value.
A company produces two products, A and B. At least 30 units of product A and at least 10 units of product B must be produced. The maximum number of units that can be produced per day is 80. Product A yields a profit of $15 and product B yields a profit of $8. Let a = the number of units of product A and b = the number of units of product B.
What objective function can be used to maximize the profit?
The vertices of the feasible region are (70, 10), (30, 10), and (30, 50). To maximize the profit, the company should produce units of product A and units of product B. The maximum profit is $
The graph shows the feasible region for the system with constraints:
y mr001-1.jpg 15 x + y mr001-2.jpg 25 x + 2y mr001-3.jpg 30
What are the vertices of the feasible region? Check all of the boxes that apply.
What is the minimum value of the objective function C = 4x + 9y?
Given the system of contstraints:
y ≥ 2x x + y ≤ 14 y ≥ 1
5x + y ≥ 14 x + y ≥ 9
Which region represents the graph of the feasible region for the given constraints?
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