Many new ventures focusing on craft beer have been launched. If the goal is to make a profit, perhaps it would have been a better choice to forget making the beer and instead focus on the hops market. There is competition for the available supply of hops, and this is especially true of the organic varieties. Cassidy Brewery uses standards to carefully track their costs. For their Hopalong label their standard for hops is 20 pounds per barrel and their standard rate is $13.00 per pound. In the past period they produced 40 barrels of their Hopalong beer using 830 pounds of hops. The hops had a cost of $15.00 per pound. Compute the total rate variance and the total efficiency variance for the past month. Also, for each variance, indicate whether the variance is favorable or unfavorable.

a. Total rate variance = $1,660 Unfavorable

b. Total efficiency variance = $450 Unfavorable

Explanation:

From the question, we have:

Standard for hops = 20 pounds per barrel

Standard rate = Standard rate for hops = $13.00 per pound

Barrels of Hopalong beer produced = 40

Actual quantity = Actual pounds of hops used = 830 pounds

Standard quantity = Standard pounds of hops = Standard for hops * Barrels of Hopalong beer produced = 20 * 40 = 800 pounds

Actual rate = Actual cost of hops per pound = $15

Therefore, we have:

a. Compute the total rate variance for the past month

Total rate variance = (Actual rate - Standard rate) * Actual quantity = ($15 - $13) * 830 = $1,660 Unfavorable

The total rate variance of $1,660 is unfavorable because the Actual rate is greater than the Standard rate.

b. Compute the total efficiency variance for the past month

Total efficiency variance = (Actual quantity - Standard quantity) * Standard rate = (830 - 800) * $15 = $450 Unfavorable

The total efficiency variance of $450 is unfavorable because the Actual quantity is greater than the Standard quantity.

the answer should be a)

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.