Kane Manufacturing produces two models of fireplace grates, model A and model B. To produce each model A grate requires 3 lbs. of cast iron and 6 minutes of labor. To produce each model B grate requires 4 lbs. of cast iron and 3 minutes of labor. The profit for each model A grate is $2.00 and the profit for each model B grate is $1.50. If the company has 1000 lbs. of cast iron and 20 labor hours available for the production of fire grates, how many of each grates of each model should be made to maximize Kane’s profit? What is the maximum profit? Write the objective function and the system of constraints. (use the graphical method of linear programming) Also, can you please make note of every single step, please! Thank you!
Kane Manufacturing produces two models of fireplace grates, model A and model B. To produce each model A grate requires 3 lbs. of cast iron and 6 minutes of labor. To produce each model B grate requires 4 lbs. of cast iron and 3 minutes of labor. The profit for each model A grate is $2.00 and the profit for each model B grate is $1.50. If the company has 1000 lbs. of cast iron and 20 labor hours available for the production of fire grates, how many of each grates of each model should be made to maximize Kane’s profit? What is the maximum profit? Write the objective function and the system of constraints. (use the graphical method of linear programming)
Also, can you please make note of every single step, please! Thank you!
Given:
| Products | Iron (lbs) | Time (minutes) | Profit ($) |
| A | 3 | 6 | 2.00 |
| B | 4 | 3 | 1.50 |
| Total | 1000 | 20(hours) | ? |
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