Starling Coating and substitution

Starling Coating produces weatherproofing coatings that protect metal from oxidation. One of Starling's patented coatings, zurtan, is composed of two inputs, magna45 and zelon. While both inputs are required, they can be substituted for each other. The following table describes how many P gallons of magna45 and zelon are required to produce a single batch of Zurtan.

Gallons of Magna45 and Zelon needed to make one batch of Zurtan
Magna 45 Zelon
1 30.00
2 15.00
3 10.00
4 7.50
5 6.00
6 5.00
7 4.30
8 3.75
9 3.33
10 3.00

In other words, one batch of zurtan can be produced using one gallon of magna45 and 30 gallons of zelon, or 2 gallons of magna45 and 15 gallons of zelon, or 3 gallons of magna45 and 10 gallons of zelon, and so forth. Starling has a long-term contract with a defense contractor to supply a fixed quantity of zurtan at a fixed price, neither of which can be altered. The price of zurtan is far above its manufacturing cost. Starling uses a standard cost system and at the beginning of the year establishes the standard quantities of the various raw materials used to manufacture its coatings.

Before Starling's fiscal year begins, management estimates that magna45 will have a standard price of $4 per gallon and zelon will have a standard price of $5 per gallon.

The manager in charge of producing zurtan has decision-making authority to alter the mix of magna45 and zelon used to produce zurtan and is evaluated and rewarded based on two criteria: meeting delivery schedules of zurtan (including quantities and quality specifications) and materials quantity variances of magna45 and zelon.

Required:
a. Before Starling's fiscal year begins, determine the cost-minimizing (standard) quantities of magna45 and zelon per batch of zurtan.
b. Soon after the fiscal year begins, the price of magna45 falls to $3 per gallon and the price of zelon rises to $7 per gallon. What are the efficient (cost-minimizing) quantities of magna45 and zelon that Starling should use to produce a batch of zurtan?
c. Starling has a policy of never changing standards during the year. Standard prices and standard quantities are changed only before the next fiscal year begins. What quantities of magna45 and zelon will the zurtan production manager choose after the price of magna45 falls to $3 per gallon and zelon rises to $7 per gallon?
d. Why doesn't Starling its policy of never changing standards after the fiscal year begins?