I need help solving these types of problems here is one one of them. Can somone show me how to solve them.thanks
Production Requirements An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 1 unit of zinc, and 2 units of glass. Each resistor requires 3, 2, and 1 units of the three materials, and each computer chip requires 2, 1, and 2 units of these materials, respectively. How many of each product can be made with the following amounts of materials?
a. 810 units of copper, 410 units of zinc, and 490 units of glass
b. 765 units of copper, 385 units of zinc, and 470 units of glass
c. 1010 units of copper, 500 units of zinc, and 610 units of glass
a. Consider how many transistors can be made, sith Copper:Glass:Zinc in a 3:2:1 ratio.
There clearly is an excess of zinc. The limiting ingredient is glass since the 810 units of copper would require 540 of glas, and there is not that much available. Using 490 units of glass, you require 245 units of zinc (1/2 x 490) and 735 units of copper (3/2 x 490)
Do the others similarly
To solve this problem, we need to determine how many of each product (transistors, resistors, and computer chips) can be made with the given amounts of materials.
Let's start with part a.
a. Given: 810 units of copper, 410 units of zinc, and 490 units of glass.
First, let's consider how many transistors can be made. The ratio of Copper:Glass:Zinc for transistors is 3:2:1. To find the limiting ingredient, we need to compare the available quantity of each material to their respective ratios.
For the copper requirement of 3 units per transistor, we have 810 units of copper. So, we can make 810 / 3 = 270 transistors.
For the glass requirement of 2 units per transistor, we have 490 units of glass. So, we can make 490 / 2 = 245 transistors.
For the zinc requirement of 1 unit per transistor, we have 410 units of zinc. So, we can make 410 / 1 = 410 transistors.
Now let's move on to resistors. The ratio of Copper:Glass:Zinc for resistors is 3:1:2.
For the copper requirement of 3 units per resistor, we have 810 units of copper. So, we can make 810 / 3 = 270 resistors.
For the glass requirement of 1 unit per resistor, we have 490 units of glass. So, we can make 490 / 1 = 490 resistors.
For the zinc requirement of 2 units per resistor, we have 410 units of zinc. So, we can make 410 / 2 = 205 resistors.
Finally, let's move on to computer chips. The ratio of Copper:Glass:Zinc for computer chips is 2:2:1.
For the copper requirement of 2 units per computer chip, we have 810 units of copper. So, we can make 810 / 2 = 405 computer chips.
For the glass requirement of 2 units per computer chip, we have 490 units of glass. So, we can make 490 / 2 = 245 computer chips.
For the zinc requirement of 1 unit per computer chip, we have 410 units of zinc. So, we can make 410 / 1 = 410 computer chips.
Therefore, with the given amounts of materials in part a, we can make 270 transistors, 270 resistors, and 405 computer chips.
You can repeat the same process for parts b and c by considering the ratios and available quantities of materials for each product.