Question

In: Economics

Incline Electronics produces three different products in a plant that is open 40 hours per week....

Incline Electronics produces three different products in a plant that is open 40 hours per week. Each product requires the following processing times (in hours) on each of three machines.

Each machine must be run by one of 19 cross-trained workers who are each available 35 hours per week. The plant has 10 type 1 machines available, 6 type 2 machines available, and 8 type 3 machines available. Products 1, 2, and 3 contribute $90, $120, and $150, respectively, in marginal profit per unit produced.

a. Select the correct LP model for this problem.

Let P₁ represent Units of product 1 to make.
Let P₂ represent Units of product 2 to make.
Let P₃ represent Units of product 3 to make.

I	MAX	90P₁ + 120P₂ + 150P₃
	ST	2P₁ + 2P₂ + 1P₃ ≤ 240
		3P₁ + 4P₂ + 6P₃ ≤ 400
		4P₁ + 6P₂ + 5P₃ ≤ 320
		9P₁ + 12P₂ + 12P₃ ≤ 665
		P_i ≥ 0

II	MIN	90P₁ + 120P₂ + 150P₃
	ST	2P₁ + 2P₂ + 1P₃ ≤ 240
		3P₁ + 4P₂ + 6P₃ ≤ 320
		4P₁ + 6P₂ + 5P₃ ≤ 400
		9P₁ + 12P₂ + 12P₃ ≤ 665
		P_i > 0

III	MIN	90P₁ + 120P₂ + 150P₃
	ST	2P₁ + 2P₂ + 1P₃ ≥ 400
		3P₁ + 4P₂ + 6P₃ ≥ 665
		4P₁ + 6P₂ + 5P₃ ≥ 320
		9P₁ + 12P₂ + 12P₃ ≥ 240
		P_i > 0

IV	MAX	90P₁ + 120P₂ + 150P₃
	ST	2P₁ + 2P₂ + 1P₃ ≤ 400
		3P₁ + 4P₂ + 6P₃ ≤ 240
		4P₁ + 6P₂ + 5P₃ ≤ 320
		9P₁ + 12P₂ + 12P₃ ≤ 665
		P_i ≥ 0

Select I,II,III,IV

b. Implement your model in a spreadsheet and solve it. How many units for each product should Incline Electronics produce? Round your answers to one decimal place, if necessary.

	Quantity
Product 1
Product 2
Product 3

c. What is the total profit for the optimal solution?
$

d. How many workers should be assigned to each type of machine? Round your answers to one decimal place, if necessary.

Machine 1
Machine 2
Machine 3

Expert Solution

a. The correct option is D.

We need to maximize revenue. Total revenue would be

90P1+120P2 + 150P3. So, maximizing constraint is

MAX 90P1+120P2 + 150P3

This leaves us with options A and D.

Now, the workers work 35 hours and there are total 19 workers. So total worker hours available is 19*35=665. Worker constraint is

9P1 + 12P2 + 12P3 ≤ 665

There are 10 Type 1 machines. The plant orks for 40 hours per week. Machine 1 hours available=40*10=400. Similarly, machine 2 hours available hours 6*40=240. Machine 3 hours available 8*40=320.

Machine constraints

2P1 + 2P2 + 1P3 ≤ 400
3P1 + 4P2 + 6P3 ≤ 240
4P1 + 6P2 + 5P3 ≤ 320

Combining all constraints, we get

Option D

B. Using solver option (In Data tab), we can solve the problem for maximum profit.
Note- if solver option is not there in your data tab, go to options and then plug-ins and enable it first.

First elts setup the problem in excel. We have already designed the problem in part A. Putting it in excel will look like this.

The quantity and profit tabs are zero right now because excel solver will determine the quantities for max profit.

Clicking on solver and then we need to enter for the following parameters.

We are maximizing profit (F3) by changing the number of units made (B2:D2) subject to constraints. Click on solve and we will get the following output.

As can be seen,

Quantity 1=6.7
Quantity 2=41.3
Quantity 3=9.2

C. Total profit, as solved in part B, is $6925

D. Workers for
Machine 1=3
Machine 2=6.9
Machine 3=9.1

Rahul Sunny answered 2 years ago

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