WorldLight Company produces two lamp fixtures (products 1 and 2) that require metal parts and electrical components. Management wants to determine how many units of each product to manufacture to maximize profit. For each unit of product 1, 1 unit of metal parts and 2 units of electrical components are required. For each unit of product 2, 3 units of metal parts and 2 units of electrical components are required. The company has 200 units of metal parts and 300 units of electrical components. Each unit of product 1 yields a profit of $1 and each unit of product 2, up to 60 units, yields a profit of $2. Any excess of 60 units of product 2 does not yield a profit, so making more than that amount is out of consideration. a) Formulate a linear programming model. b) Use the graphical method to solve this model. What is the resulting total profit?
WorldLight Company produces two lamp fixtures (products 1 and 2) that require metal parts and electrical components. Management wants to determine how many units of each product to manufacture to maximize profit. For each unit of product 1, 1 unit of metal parts and 2 units of electrical components are required. For each unit of product 2, 3 units of metal parts and 2 units of electrical components are required. The company has 200 units of metal parts and 300 units of electrical components. Each unit of product 1 yields a profit of $1 and each unit of product 2, up to 60 units, yields a profit of $2. Any excess of 60 units of product 2 does not yield a profit, so making more than that amount is out of consideration.
a) Formulate a linear programming model.
b) Use the graphical method to solve this model. What is the resulting total profit?
![3.1-8. La compañía WorldLight produce dos dispositivos para lám-
paras (productos 1 y 2) que requieren partes de metal y componentes
eléctricos. La administración desea determinar cuántas unidades de
cada producto debe fabricar para maximizar la ganancia. Por cada
unidad del producto 1 se requieren 1 unidad de partes de metal y 2
unidades de componentes eléctricos. Por cada unidad del producto
2 se necesitan 3 unidades de partes de metal y 2 unidades de compo-
nentes eléctricos. La compañía tiene 200 unidades de partes de metal
y 300 de componentes eléctricos. Cada unidad del producto 1 da una
ganancia de $1 y cada unidad del producto 2, hasta 60 unidades, da
una ganancia de $2. Cualquier exceso de 60 unidades del producto
2 no genera ganancia, por lo que fabricar más de esa cantidad está
fuera de consideración.
a) Formule un modelo de programación lineal.
D.I b) Utilice el método gráfico para resolver este modelo. ¿Cuál es
la ganancia total que resulta?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6616954c-f145-46cf-a687-0d4e31796a85%2F91cef3df-de46-449e-8ad5-c7e68d8d1a26%2Fmo8mgqb_processed.png&w=3840&q=75)
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