The demand function for the luminar desk lamp is given by p = f(x) = −0.1x2 − 0.3x + 20 where x is the quantity demanded in thousands and p is the unit price in dollars. (a) find f '(x). f '(x) = −.2x−.3 (b) what is the rate of change of the unit price when the quantity demanded is 7000 units (x = 7)? $ per 1000 lamps what is the unit price at that level of demand

Buyer henry is going to accept seller shannon's $282,500 counteroffer. when will this counteroffer become a contract. a. counteroffers cannot become contracts b. when henry gives shannon notice of the acceptance c. when henry signs the counteroffer d. when shannon first made the counteroffer

Ashop owner uses a reorder point approach to restocking a certain raw material. lead time is six days. usage of the material during lead time is normally distributed with a mean of 42 pounds and a standard deviation of four pounds. when should the raw material be reordered if the acceptable risk of a stockout is 3 percent?

Anew firm is developing its business plan. it will require $615,000 of assets, and it projects $450,000 of sales and $355,000 of operating costs for the first year. management is reasonably sure of these numbers because of contracts with its customers and suppliers. it can borrow at a rate of 7.5%, but the bank requires it to have a tie of at least 4.0, and if the tie falls below this level the bank will call in the loan and the firm will go bankrupt. what is the maximum debt ratio the firm can use? (hint: find the maximum dollars of interest, then the debt that produces that interest, and then the related debt ratio.)a. 41.94%b. 44.15%c. 46.47%d. 48.92%e. 51.49%