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. Inventories An electronics store manager stocks from 20 to 30 IBM-compatible computers and from 30 to 50 Apple computers. There is room in the store to stock up to 60 computers. The manager receives a commission of $\$ 50$ on the sale of each IBM-compatible computer and $\$ 40$ on the sale of each Apple computer. If the manager can sell all of the computers, how many should she stock to maximize her commissions? Find the maximum commission. $$\begin{array}{|lcc|} \hline \text { Inventory } & \text { IBM } & \text { Apple } \\ \hline \text { Minimum } & 20 & 30 \\ \text { Maximum } & 30 & 50 \\ \text { Commission } & \$ 50 & \$ 40 \\ \hline \end{array}$$
Added by Christopher D.
Step 1
Define the variables: Let $x$ be the number of IBM-compatible computers and $y$ be the number of Apple computers. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Allison Knapp and 85 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
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. A diet requires at least 16 units of vitamin $C$ and at least 34 units of vitamin $B$ complex. Two food supplements are available that provide these nutrients in the amounts and costs shown in the table. How much of each should be used to minimize the cost? $$\begin{array}{|c|c|c|c|} \hline \text { Supplement } & \begin{array}{c} \text { Vitamin } \\ \text { C } \end{array} & \begin{array}{c} \text { Vitamin } \\ \text { B } \end{array} & \text { cost } \\ \hline \mathrm{A} & 3 \text { units/g } & 2 \text { units/g } & 3 \mathrm{?} / \mathrm{g} \\ \mathrm{B} & 2 \text { units/g } & 6 \text { units/g } & 4 \mathrm{?} / \mathrm{g} \\ \hline \end{array}$$
Linear Systems
Linear Programming
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)
H M.
Sketch the region corresponding to the system of constraints. Then find the minimum and maximum values of the objective function (if possible) and the points where they occur, subject to the constraints. Objective function: $z=4 x+5 y$ Constraints: $$x \geq 0$$$y \geq 0$$x+y \geq 8$$3 x+5 y \geq 30$
Systems of Equations and Inequalities
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Watch the video solution with this free unlock.
EMAIL
PASSWORD