Acompany wants to develop a level production. the beginning inventory is 4. demand for the next four periods is given in what follows. 1) what production rate per period will give a zero inventory at the end of period 1? 2) when and in what quantities will backorders occur? 3) what level production rate per period will avoid backorders? then what will be the ending inventory in period 4? 4) if the cost of carrying inventory is $5 per unit per period and stockout cost $ 50 per unit, what will be the total cost of the plan developed in 4.1)? 5) what will be the cost of the plan developed in 4.3)? 6) which is the better production plan between 4.1) and 4.3)? explain why.

Suppose you win a small lottery and have the choice of two ways to be paid: you can accept the money in a lump sum or in a series of payments over time. if you pick the lump sum, you get $2,950 today. if you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. 1) at an interest rate of 6% per year, the winner would be better off accepting the (lump sum / payments over time), since it has the greater present value. 2) at an interest rate of 9% per year, the winner would be better off accepting the (lump sum / payments over time), since it has the greater present value. 3) years after you win the lottery, a friend in another country calls to ask your advice. by wild coincidence, she has just won another lottery with the same payout schemes. she must make a quick decision about whether to collect her money under the lump sum or the payments over time. what is the best advice to give your friend? a) the lump sum is always better. b) the payments over time are always better. c) it will depend on the interest rate; advise her to get a calculator. d) none of these answers is good advice.

In william rathje's garbology project that focused on household waste, front door interviews found 15 percent of respondents saying that they consumed beer. the trash discard from the same area showed what percentage of household's consuming beer

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.