Amad was curious if triangles \triangle ABC△ABCtriangle, A, B, C, and \triangle EDF△EDFtriangle, E, D, F were congruent. He was
able to map one figure onto the other using a reflection and a rotation. Amad concluded: "I was able to map \triangle ABC△ABCtriangle, A, B, C onto \triangle EDF△EDFtriangle, E, D, F using a sequence of rigid transformations, so the figures are congruent."
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Let "c" and "q" represent the numbers of bottles of Classic and Quantum that should be produced each day to maximize profit. The problem conditions give rise to 3 inequalities:
.. 0.500c +0.550q ≤ 100 . . . . . . . liters of water
.. 0.600c +0.200q ≤ 100 . . . . . . . kg of sugar
.. 0.1c +0.2q ≤ 32 . . . . . . . . . . . . . grams of caramel
These can be plotted on a graph to find the feasible region where c and q satisfy all constraints. You find that the caramel constraint does not come into play. The graph below has c plotted on the horizontal axis and q plotted on the vertical axis.
Optimum production occurs near c = 152.17 and q = 43.48. Examination of profit figures for solutions near those values reveals the best result for (c, q) = (153, 41). Those levels of production give a profit of 6899p per day.
To maximize profit, Cartesian Cola should produce each day
.. 153 bottles of Classic
.. 41 bottles of Quantum per day.
Profit will be 6899p per day.
_____
The problem statement gives no clue as to the currency equivalent of 100p.
.. 0.500c +0.550q ≤ 100 . . . . . . . liters of water
.. 0.600c +0.200q ≤ 100 . . . . . . . kg of sugar
.. 0.1c +0.2q ≤ 32 . . . . . . . . . . . . . grams of caramel
These can be plotted on a graph to find the feasible region where c and q satisfy all constraints. You find that the caramel constraint does not come into play. The graph below has c plotted on the horizontal axis and q plotted on the vertical axis.
Optimum production occurs near c = 152.17 and q = 43.48. Examination of profit figures for solutions near those values reveals the best result for (c, q) = (153, 41). Those levels of production give a profit of 6899p per day.
To maximize profit, Cartesian Cola should produce each day
.. 153 bottles of Classic
.. 41 bottles of Quantum per day.
Profit will be 6899p per day.
_____
The problem statement gives no clue as to the currency equivalent of 100p.
Answer:
Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
