I feel struggled about the following problem

Bob has been assigned two problem sets in his Microeconomics subject, Assignments 1 and 2, which he has already spent some time on, but has not nished yet. They are due in 12 hours; Bob cares a lot about his mark in Microeconomics and is willing to spend all these 12 hours on two assignments. There is still some room for improvement in his assignments; let us denote a unit of improve- ment for Assignment 1 by 21; and by 2'2 for Assignment 2. Assignment 1 is twice as difcult as Assignment 2. To improve Assignment 2 by one unit, Bob needs to spend it 6 ([1,5] hours; to improve Assignment 1 by one unit, Bob needs to spend 2t hours (t is a parameter which you treat as a xed number; if t is confusing, start solving the problem by assuming :5 = 1). Bob knows that Assignment 1 is already quite good (indeed, it has been assigned long time ago) and return on improvement there is diminishing fast. There is some more work to be done on Assignment 2. That is, he knows that improvements will lead to increase in his mark according to the following \"production function:\" m(z'1,z'2) = a + i2 (this function captures the notion that Assignment 1 is already good and improvements there will not lead to a signicant increase in the mark, while improvements in Assignment 2 will). (a) Write this problem as Bob's constrained optimisation problem. (b) What is Bob's optimal time allocation between two assignments? (Your answer may depend on t.)