Question

Jond sells pottery as a side job. He makes bowls and cups, both of which require shaping and firing. Each Dowi requires 1 hour to shape and 2 hours to fire, while creating a cup requires 3 hours to shape and 2 hour to fire. John has at most 15 hours to shape and less than 14 hours to fire each weekend. John makes $ 8 in profit on each bowl and $11 profit on each cup. 2. Write a system of inequalities expressing these conditions (3 pts.) and graph the feasible region (4 pts.). Then, estimate the combination of bowls and cups that will produce the most profit (3 pts.) her

Answer 1

Let the number of bowls be B and number of cups be C.

Therefore total hours required for shaping of bowl be B×1 and total hours required for firing of bowl be 2×B.

Total hours required to shape a cup be 3×C and fire a cup be 2×C.

As per the total number of hours available for shaping and firing the inequality become :

B + 3C <= 15 2B + 2C <= 14

Profit on each bowl is 8 and on cup is 11.

Now we have to maximize 8B + 11C subject to the above two constraints .

Plot the Constraints with an equality. The shaded side of the lines represent the feasible portion of that inequality. The shaded region in blue represents the feasible region given the two constraints. The two constraints intersect at ( 3,4 ). It represents the optimal solution of the given profit maximization problem. The highest level of profit 8B+11C is obtained at this point. And maximum profit is 68. So the line 8B + 11 C = 68 has been plotted depicting the highest level of profit obtainable.

834116 B4 30 =15 29729 WWW 3 4 6 8 10 12 14 16