Consider the following production function for a firm: q = 200L0.75 K0.25 where q= output, K = capital and L = labor. The firm uses capital and labor whose prices are $60 and $30 respectively. The total cost outlay for the utilizations of both capital and labor is $8,400. Using the Lagrangian Multiplier procedure, determine the amount of each input to use, which will maximize output.

James albemarle created a trust fund at the beginning of 2016. the income from this fund will go to his son edward. when edward reaches the age of 25, the principal of the fund will be conveyed to united charities of cleveland. mr. albemarle specified that 75 percent of trustee fees are to be paid from principal. terry jones, cpa, is the trustee. james albemarle transferred cash of $500,000, stocks worth $400,000, and rental property valued at $250,000 to the trustee of this fund. immediately invested cash of $360,000 in bonds issued by the u.s. government. commissions of $7,900 are paid on this transaction. incurred permanent repairs of $9,000 so that the property can be rented. payment is made immediately. received dividends of $8,000. of this amount, $3,000 had been declared prior to the creation of the trust fund. paid insurance expense of $4,000 on the rental property. received rental income of $10,000. paid $8,000 from the trust for trustee services rendered. conveyed cash of $7,000 to edward albemarle.

The assumptions of the production order quantity model are met in a situation where annual demand is 3650 units, setup cost is $50, holding cost is $12 per unit per year, the daily demand rate is 10 and the daily production rate is 100. the production order quantity for this problem is approximately:

Now ray has had the tires for two months and he notices that the tread has started to pull away from the tire. he has already contacted the place who sold the tires and calmly and accurately explained the problem. they didn’t him because they no longer carry that tire. so he talked with the manager and he still did not get the tire replaced. his consumer rights are being violated. pretend you are ray and write a letter to the company’s headquarters. here are some points to keep in mind when writing the letter: include your name, address, and account number, if appropriate. describe your purchase (name of product, serial numbers, date and location of purchase). state the problem and give the history of how you tried to resolve the problem. ask for a specific action. include how you can be reached.