Auto pistons at wemming chung's plant in shanghai are a produced in a forging process, and the diameter is a critical factor that must be controlled. from sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) what is the value of x ? b) what is the value of r? c) what are the ucl and lclx, using 3 sigma? plot the data. d) what are the uclr and lclr, using 3u? plot the data. e) if the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new uclx and lclx?

At a student café, there are equal numbers of two types of customers with the following values. the café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., she cannot price-discriminate). students with early classes students without early classes coffee 70 60 banana 51 101 the marginal cost of coffee is 10 and the marginal cost of a banana is 40. the café owner is considering three pricing strategies: 1. mixed bundling: price bundle of coffee and a banana for 161, or just a coffee for 70. 2. price separately: offer coffee at 60, price a banana at 101. 3. bundle only: coffee and a banana for 121. do not offer goods separately. assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle. for simplicity, assume there is just one student with an early class, and one student without an early class. price strategy revenue from pricing strategy cost from pricing strategy profit from pricing strategy 1. mixed bundling $ $ $ 2. price separately $ $ $ 3. bundle only $ $ $ pricing strategy yields the highest profit for the café owner.

Suppose the production function in an economy is y = k0.5l0.5, where k is the amount of capital and l is the amount of labor. the economy begins with 64 units of capital and 16 units of labor. use a calculator and equations in the chapter to find a numerical answer to each of the following questions. what are the wage and the rental price of capital? the wage is equal to unit(s) of output and the rental price of capital is equal to unit(s) of output.

Afirm wants to strengthen its financial position. which of the following actions would increase its current ratio? a. reduce the company's days' sales outstanding to the industry average and use the resulting cash savings to purchase plant and equipment.b. use cash to repurchase some of the company's own stock.c. borrow using short-term debt and use the proceeds to repay debt that has a maturity of more than one year.d. issue new stock, then use some of the proceeds to purchase additional inventory and hold the remainder as cash.e. use cash to increase inventory holdings.