Why do some students take out private loans when they are eligible for federal student loans at much lower interest rates?
a. private loans have much lower fees.
b. they are probably not aware of the rate difference and of their eligibility for the federal loans.
c. private loans don't have to be repaid for 10 years.
d. private loans favor students with very low incomes.

Acompany manufactures x units of product a and y units of product b, on two machines, i and ii. it has been determined that the company will realize a profit of $3 on each unit of product a and $4 on each unit of product b. to manufacture a unit of product a requires 7 min on machine i and 5 min on machine ii. to manufacture a unit of product b requires 8 min on mchine i and 5 min on machine ii. there are 175 min available on machine i and 125 min available on machine ii in each work shift. how many units of a product should be produced in each shift to maximize the company's profit p?