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The table below summarizes the production rates of two machines for two products in a factory.Production rate for Product A(units per hour)Production Rate for Product B(units per hour)Machine 1 50 80Machine 2 50 20The cost per hour to operate machines 1 and 2 are Php 2500.00 and Php 1500.00 respectively.© 2020 Philippine Science High School System. All rights reserved. This document may contain proprietary information and may only bereleased to third parties with approval of management. Document is uncontrolled unless otherwise marked; uncontrolled documentsare not subject to update notification.*TA – time allocation suggested by the teacher Mathematics 2 |Page 4 of 6 **ATA – actual time allocation spent by the student (for information purposes only)If the production schedule requires at least 250 units of product A and at least 160 unitsproduct B be produced during each day, how long should each machine run to minimize operationcosts? (Sullivan, 2012, 929)

Question

The table below summarizes the production rates of two machines for two products in a factory.Production rate for Product A(units per hour)Production Rate for Product B(units per hour)Machine 1 50 80Machine 2 50 20The cost per hour to operate machines 1 and 2 are Php 2500.00 and Php 1500.00 respectively.© 2020 Philippine Science High School System. All rights reserved. This document may contain proprietary information and may only bereleased to third parties with approval of management. Document is uncontrolled unless otherwise marked; uncontrolled documentsare not subject to update notification.*TA – time allocation suggested by the teacher Mathematics 2 |Page 4 of 6 **ATA – actual time allocation spent by the student (for information purposes only)If the production schedule requires at least 250 units of product A and at least 160 unitsproduct B be produced during each day, how long should each machine run to minimize operationcosts? (Sullivan, 2012, 929)

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Solution

To minimize operation costs, we need to determine the optimal running time for each machine.

Let's start by calculating the total production capacity of each machine for both products.

For Machine 1, the production rate for Product A is 50 units per hour, and for Product B is 80 units per hour. So, in one hour, Machine 1 can produce 50 units of Product A and 80 units of Product B.

For Machine 2, the production rate for Product A is 50 units per hour, and for Product B is 20 units per hour. So, in one hour, Machine 2 can produce 50 units of Product A and 20 units of Product B.

Now, let's determine the minimum running time required for each machine to meet the production schedule.

For Product A, we need at least 250 units to be produced each day. Since Machine 1 can produce 50 units per hour, it would take 250/50 = 5 hours to produce 250 units of Product A using Machine 1. Similarly, Machine 2 can also produce 50 units per hour, so it would also take 250/50 = 5 hours to produce 250 units of Product A using Machine 2.

For Product B, we need at least 160 units to be produced each day. Machine 1 can produce 80 units per hour, so it would take 160/80 = 2 hours to produce 160 units of Product B using Machine 1. Machine 2 can produce 20 units per hour, so it would take 160/20 = 8 hours to produce 160 units of Product B using Machine 2.

Now, let's calculate the operation costs for each machine.

The cost per hour to operate Machine 1 is Php 2500.00, and for Machine 2 is Php 1500.00.

For Machine 1, the total operation cost would be 5 hours * Php 2500.00 = Php 12500.00.

For Machine 2, the total operation cost would be 8 hours * Php 1500.00 = Php 12000.00.

Therefore, to minimize operation costs, Machine 2 should run for 8 hours to produce 160 units of Product B, and Machine 1 should run for 5 hours to produce 250 units of Product A.

This problem has been solved

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