Question

A chemical company produces a special industrial chemical that is a blend of three chemical ingredients. The beginning-year cost per pound, the ending-year cost per pound, and the blend proportions follow. (Round your answers to the nearest integer.) Cost per Pound ($) Ingredient Beginning Ending Quantity (pounds) per 100 Pounds of Product A 2.50 2.95 25 B 8.75 9.90 10 C 0.99 0.90 60 (a) Compute the price relatives for the three ingredients. Item Price Relative A B C

Answer 1

The item price relative of ingredients A, B and C is 118, 113 and 91

Step-by-step explanation:

Given

-----------------Cost per Pound ($)

Ingredient ---- Beginning ------ Ending Quantity (pounds) per 100 Pounds of Product

A ---------------- 2.50 ------ 2.95 ------ 25

B ---------------- 8.75 ------ 9.90 ------- 10

C ----------------- 0.99 ----- 0.90 ----- 60

Required

Calculate the price relatives for all ingredients

The price relatives for each ingredient is calculated using the following formula.

Price Relative = (P' * Q)/P°

Where

P' = Ending Cost per pound

P° = Beginning Cost per pound

Q = Quantity

The quantity is uniform for all products because it's measured per 100 pounds of each product.

So, Q = 100

Calculating Price Relative of A

P' of Ingredient A = 2.95

P° of Ingredient A = 2.50

By Substituting the right values in the given formula

P = (2.95 * 100)/2.50

P = 295/2.50

P = 118

Calculating Price Relative of B

P' of Ingredient B = 9.90

P° of Ingredient B = 8.75

By Substituting the right values in the given formula

P = (9.90 * 100)/8.75

P = 990/8.75

P = 113.1429

P = 113 ( Approximated)

Calculating Price Relative of C

P' of Ingredient C = 0.9

P° of Ingredient C = 0.99

By Substituting the right values in the given formula

P = (0.9 * 100)/0.99

P = 90/0.99

P = 90.90909

P = 91 (Approximated).

Hence, the item price relative of ingredients A, B and C is 118, 113 and 91