A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8.70 per stone for quantities of 600 stones or more, $9.20 per stone for orders of 400 to 599 stones, and $10.00 per stone for lesser quantities. The jewelry firm operates 109 days per year. Usage rate is 25 stones per day, and ordering costs are $48.

a. If carrying costs are $2 per year for each stone, find the order quantity that will minimize total annual cost.
Order quantitystones
b. If annual carrying costs are 29 percent of unit cost, what is the optimal order size?
c. If lead time is 3 working days, at what point should the company reorder?

Newton industries is considering a project and has developed the following estimates: unit sales = 4,800, price per unit = $67, variable cost per unit = $42, annual fixed costs = $11,900. the depreciation is $14,700 a year and the tax rate is 34 percent. what effect would an increase of $1 in the selling price have on the operating cash flow?

Alarge tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.

Laval produces lamps and home lighting fixtures. its most popular product is a brushed aluminum desk lamp. this lamp is made from components shaped in the fabricating department and assembled in the assembly department. information related to the 22,000 desk lamps produced annually follows.direct materials $280,000direct labor fabricating department (8,000 dlh × $24 per dlh) $192,000assembly department (16,600 dlh × $26 per dlh) $431,600machine hours fabricating department $15,200mhassembly department $20,850mhexpected overhead cost and related data for the two production departments follow.fabricating assemblydirect labor hours 150,000dlh 295,000dlhmachine hours 161,000mh 128,000mhoverhead cost $400,000 430,000required1. determine the plantwide overhead rate for laval using direct labor hours as a base.2. determine the total manufacturing cost per unit for the aluminum desk lamp using the plantwide overhead rate.3. compute departmental overhead rates based on machine hours in the fabricating department and direct labor hours in the assembly department.4. use departmental overhead rates from requirement 3 to determine the total manufacturing cost per unit for the aluminum desk lamps.