at what stage of the product life cycle would it be best to begin investing in research and development of the next product?

Bandar industries berhad of malaysia manufactures sporting equipment. one of the company’s products, a football helmet for the north american market, requires a special plastic. during the quarter ending june 30, the company manufactured 35,000 helmets, using 22,500 kilograms of plastic. the plastic cost the company $171,000. according to the standard cost card, each helmet should require 0.6 kilograms of plastic, at a cost of $8 per kilogram. 1. what is the standard quantity of kilograms of plastic (sq) that is allowed to make 35,000 helmets? 2. what is the standard materials cost allowed (sq x sp) to make 35,000 helmets? 3. what is the materials spending variance? 4. what is the materials price variance and the materials quantity variance?

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.

You wish to retire in 13 years, at which time you want to have accumulated enough money to receive an annual annuity of $23,000 for 18 years after retirement. during the period before retirement you can earn 9 percent annually, while after retirement you can earn 11 percent on your money. what annual contributions to the retirement fund will allow you to receive the $23,000 annuity? use appendix c and appendix d for an approximate answer, but calculate your final answer using the formula and financial calculator methods.