MATHEMATICS COLLEGE

A company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A and B. However, the company cannot sell more than 110 units of A per day. Both products use one raw material, of which the maximum daily availability is 300 lb. The usage rates of the raw material are 2 lb per unit of A, and 4 lb per unit of B The profit units for A and B are $40 and $90, respectively. Determine the optimal product mix for the company

Answers

Answer 1

Answer:

Answer:A=100 , b=25

Step-by-step explanation:

Let sales of A be x and sales of B be y

Thus $x\geq 0.8(x+y)$

$x\geq 4y$

Also maximum A available is $110\geq x$

$300\geq 2x+4y$

$150\geq x+2y$

We have find the optimal solution for

z=40x+90y

Optimal solution points

(100,25) z $=40* 100+90* 25=6250$

(110,20) z $=40* 110+90* 20=6200$

(110,0) z $=40* 110+90* 0=4400$

Thus for A=100 and B=25 Optimal solution is obtained

Answer 2

Answer:

Final answer:

The optimal product mix problem involves maximizing profit given certain constraints. The constraints can be expressed in terms of inequalities which can be solved using linear programming techniques such as the corner point theorem or the simplex method.

Explanation:

The subject of this problem is to determine the optimal product mix of two products, A and B, produced by a company. This is guided by several constraints including sales volumes, maximum output, raw material availability, and profit units.

From the problem, we have two constraints. Firstly, sales of A must be at least 80% of the total sales of A and B, and no more than 110 units of A can be sold per day. Secondly, the company cannot use more than 300 lbs of the raw material per day with usage rates of 2 lbs per unit of A and 4 lbs per unit of B.

Let the quantity of A and B sold per day be x and y respectively. The profit is given by the expression 40x + 90y. We need to maximize this expression based on the constraints. The constraints can be expressed as follows:

x ≥ 0.8(x + y), this is the sales volume constraint.
x ≤ 110, this is the maximum sales constraint.
2x + 4y ≤ 300, this constraint arises from the raw material availability.

These constraints form a linear programming problem. By plotting these inequalities on a graph and finding the feasible region, we can use the corner point theorem or simplex method to find the optimal solution.

Learn more about Optimal Product Mix here:

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Answers

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Step-by-step explanation:

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Answers

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Answers

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

We are tasked with the following activities

Conjecture: How many solutions do $x^3 - 5x^2 + 28 = 0$ have?

Find the real solution(s) of the equation.

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A picture showing the polynomial long division method used for solving the polynomial equation and other solution(s) can be found in the attached file below.

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