Could you please help me with the following question... while the minimum demand

Question

Could you please help me with the following question...

while the minimum demand of each product is predicted to be 270 units

Do NOT use any Integer restrictions.

____ Units of product Alpha

___ Units of product Beta

The total profit contribution is _____ dollars.

A company produces product Alpha and product Beta. Each unit of product alpha requires 17 pounds of material and 0.35 labor hour Each unit of prodyct Beta requires 20 pounds of material and 0.6 labor hours The material and labor cost id $140 for each unit of Alpha while the material and labor cost $210 for each unit Beta. The unit selling price for Alpha is $270 and the unit selling price for beta is $400. The Maximum demand for each product is predicted to be 550 units

while the minimum demand of each product is predicted to be 270 units

There are 18000 pounds of material and 470 labor hours avaliable. How many units of Alpha and how many units of Beta should the company produce to maximize its total profit margin while fulfilling the demand? Use the linear programming model and use solver to find the optimal solution

Do NOT use any Integer restrictions.

____ Units of product Alpha

___ Units of product Beta

The total profit contribution is _____ dollars.

CAN YOU PLEASE SHOW ME HOW TO PUT THIS IN EXCEL STEP BY STEP USING THE OPTIMAL SOULUTION FROM SOLVER

Explanation / Answer

Let our decision variables are A representing quantity of product Alpha and B be the quantity of product Beta.

Objective is to have Maximum Profit, say Z = (210-140)A + (400-270)B = 70A + 130B

Note Profit per unit = Price per unit - Material and labor costs per unit

Constraints are in terms of avalability of materials, labor hours, and demand for the products.

Formulation and solution using excel solver is as follows:

Solution is as follows:

Number of Alpha product = 400

Number of Beta product = 550

The Total Maximum Profit = $99,500

For solver the Objective is the cell under SumProduct for Profit row Target cell, Max

Variable to be manipulated (to find/ to change) are the cells in value row under A and B -Changing cells

Constraints are having columns of SumProducts, Sign, and RHS

Options are Assume Linear Model and Assume Non-negative

Decision Variables A B Values of DecVar SumProduct Objective-Max.Profit 70 130 Maximise 70A+130B Constraints Sign RHS Material 17 20 <= 18000 17A+20B <= 18000 Labor 0.35 0.6 <= 470 .35A+.6B <=470 A-Demand - Maximum 1 0 <= 550 A <= 550 A-Demand - Minimum 1 0 >= 270 A >= 270 B-Demand - Maximum 0 1 <= 550 B <= 550 B-Demand - Minimum 0 1 >= 270 B >= 270

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