You are given the following total utilities of apples and mineral water obtained by
Bervin. Given that each apple cost K5 each bottle of water cost K2, and Bervin's
income is K22,
find the optimal combination of apples and bottles of mineral
water

2 apples and 6 bottles of water

Explanation:

since Bervin earns K22, her consumption possibilities frontier is:

apple                water                  total utils obtained

4 units               1 unit                   90 + 20 = 110 utils

3 units               3 units                75 + 54 = 129 utils

2 units               6 units                55 + 90 = 145 utils

1 unit                  8 units                30 + 98* = 128 utils

0 units               11 units                0 + 98* = 98 utils

The optimal combination of apples and bottles of water is 2 apples and 6 bottles of water because that combination yields the most utils.

*Since the table only states the utils obtained until the 7th unit, we must assume that any additional unit consumed will provide 0 utils.

among other factors, composers started writing dynamic markings in their scores because "new instruments allowed for more dynamic ranges and contrast."

dynamics allude to the loudness or softness of music. dynamics offer an approach to demonstrate articulation in sheet music. they to drive the enthusiastic substance of music through volume and force. maybe you could alter both the volume and the shading profundity on your screen at the same time. we can likewise think about the force side of elements as the quality of a note. a few notes are intended to be played delicately and gently, while others are intended to be played all the more firmly.  

some dynamics markings have a letter 'm,' which remains for mezzo, signifying 'medium.' so a mezzo piano unique stamping resembles this (mp) and intends to play medium calm, while a mezzo specialty dynamic resembles this (mf) and intends to play medium loud.