Develop an optimization model involving product mix and transportation.

Product is manufactured at A and B. A has capacity to produce 10 gallons. A requires 0.5 hour per gallon to manufacture product. A's manufacturing cost is $30 per gallon. B has capacity to produce 20 gallons. B requires 1 hour per gallon to manufacture product. B's manufacturing cost is $40 per gallon. Total manufacturing time available (accounting for both A and B) is 23 hours.

Product is sold at stores X and Y. Each store demands any amount of product between 5 and 10 gallons, inclusive. The stores do not have to each receive the same amount. X's revenue is $100 per gallon. Y's revenue is $150 per gallon. All product gets sold.

Transportation cost from A to X is $1 per gallon. Transportation cost from A to Y is $2 per gallon. Transportation cost from B to X is $6 per gallon. Transportation cost from B to Y is $7 per gallon.

Profit is revenue minus manufacturing cost minus transportation cost.

Develop a linear optimization model of this business situation to maximize profit. 

i) There are ______ decision variables? 

ii) There are ______ constraints, including the non-negativity constraints?