Business High School

A chain saw requires 2 hours of assembly and a wood chipper 6 hours. A maximum of 24 hours of assembly time is available. The profit is $150 on a chain saw and $240 on a chipper. How many of each should be assembled for maximum profit? To attain the maximum profit, assemble....... chain saws and ............wood chippers.

Answers

Answer 1

Answer:

To attain the maximum profit, assemble 9 chain saws and 1 wood chipper.

Step-by-Step Explanation:

To find the number of chain saws and wood chippers that should be assembled for maximum profit, we can set up a linear programming problem.

Let's assume x represents the number of chain saws to be assembled, and y represents the number of wood chippers to be assembled.

We have the following constraints:

1) Assembly time constraint: 2x + 6y ≤ 24 (maximum of 24 hours of assembly time available)

2) Non-negativity constraint: x ≥ 0, y ≥ 0 (we cannot have negative quantities)

We want to maximize the profit, which is given by the objective function:

Profit = 150x + 240y

To solve this linear programming problem, we can use graphical or algebraic methods. Here, we will use algebraic methods.

First, let's graph the feasible region determined by the constraints:

The assembly time constraint can be rewritten as:

2x + 6y ≤ 24

x + 3y ≤ 12

y ≤ (12 - x)/3

Next, we plot the boundary lines and shade the feasible region:

Feasible region:

x ≥ 0 (non-negativity constraint)

y ≥ 0 (non-negativity constraint)

y ≤ (12 - x)/3 (assembly time constraint)

Based on the graph, we can see that the feasible region is a triangular region bounded by the x-axis, y-axis, and the line y = (12 - x)/3.

To find the vertices of this feasible region, we can solve the equations:

x = 0

y = 0

y = (12 - x)/3

Solving these equations, we find the vertices:

(0, 0)

(0, 4)

(6, 0)

(9, 1)

Now, we evaluate the objective function (Profit = 150x + 240y) at each vertex to determine the maximum profit:

At (0, 0): Profit = 150(0) + 240(0) = 0

At (0, 4): Profit = 150(0) + 240(4) = 960

At (6, 0): Profit = 150(6) + 240(0) = 900

At (9, 1): Profit = 150(9) + 240(1) = 1,710

The maximum profit is attained at (9, 1), which means assembling 9 chain saws and 1 wood chipper will result in the maximum profit.

To attain the maximum profit, assemble 9 chain saws and 1 wood chipper.

Related Questions

A physician or surgeon may not accept or agree to accept any payment, fee, reward or anything of value for soliciting patients or patronage for any physician or surgeon. A violation constitutes a Class A misdemeanor and each payment, reward, or fee or agreement to accept a reward or fee is a separate offense.

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The given statement explains that physicians or surgeons cannot accept any form of payment, fee, reward, or anything of value in exchange for soliciting patients or patronage for other physicians or surgeons.

This rule aims to prevent unethical practices in the medical field. Violating this rule is considered a Class A misdemeanor, and each instance of accepting a payment, reward, or fee or agreeing to accept one is considered a separate offense.

In simpler terms, it means that doctors cannot receive any sort of compensation for referring patients to other doctors. This is to ensure that medical decisions are made based on the best interests of the patient, rather than financial gain. If doctors do accept such payments or rewards, they can face legal consequences.To summarize, the rule prohibits physicians and surgeons from accepting any form of payment in exchange for referring patients to other doctors, as this can compromise the integrity of medical decision-making.

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