Percy consumes cakes and ale. His demand function for cakes is qc = m − 30pc + 20pa, where pa is the price of ale, and pc is the price of cakes, and qc is his consumption of cakes. Percy’s income is $100, and the price of ale is $1 per unit.(a) Is ale a substitute for cakes or a complement?(b) Write an equation for Percy's demand function for cakes where income and the price of ale are held fixed at $100 and $1 respectively.(c) Write an equation for Percy's inverse demand function for cakes where income is $100 and the price of ale remains at $1.

Lipman auto parts, a family-owned auto parts store, began january with $10,300.00 in cash. management forecasts that collections from credit customers will be $11,400.00 in january and $14,800.00 in february. the store is scheduled to receive $5,000.00 in cash on a business note receivable in january. projected cash payments include inventory purchases ($13,000.00 in january and $13,600.00 in february) and operating expenses ($2,700.00 each month). lipman auto parts' bank requires a $10,000.00 minimum balance in the store's checking account. at the end of any month when the account balance dips below $10,000.00, the bank automatically extends credit to the store in multiples of $1,000.00. lipman auto parts borrows as little as possible and pays back loans in quarterly installments of $2,000.00, plus 4 percent interest on the entire unpaid principal. the first payment occurs three months after the loan.