When capital is plotted on the vertical axis and labor is plotted along the horizontal axis, the marginal rate of technical substitution (mrts) of labor for capital along a convex isoquant

a. equals the negative of the slope of the isoquant.

b. equals the marginal product of labor divided by the marginal product of capital.

c. declines as more and more labor is used.

d. all of the above are correct.

e. only answers a and b are correct.

Atoy manufacturer makes its own wind-up motors, which are then put into its toys. while the toy manufacturing process is continuous, the motors are intermittent flow. data on the manufacture of the motors appears below.annual demand (d) = 50,000 units daily subassembly production rate = 1,000setup cost (s) = $85 per batch daily subassembly usage rate = 200carrying cost = $.20 per unit per year(a) to minimize cost, how large should each batch of subassemblies be? (b) approximately how many days are required to produce a batch? (c) how long is a complete cycle? (d) what is the average inventory for this problem? (e) what is the total annual inventory cost (holding plus setup) of the optimal behavior in this problem?

The economic advisor of a large tire store proposes the demand function d(p)equalsstartfraction 1900 over p minus 40 endfraction , where d(p) is the number of tires of one brand and size that can be sold in one day at price p. answer parts (a) through (e) below. a. recalling that the demand must be positive, what is the domain of this function? the domain consists of all possible values of ▼ for which ▼ p d(p) ▼ does not exist. is positive. is zero. is negative. exists.

This exercise illustrates that poor quality can affect schedules and costs. a manufacturing process has 130 customer orders to fill. each order requires one component part that is purchased from a supplier. however, typically, 3% of the components are identified as defective, and the components can be assumed to be independent. (a) if the manufacturer stocks 130 components, what is the probability that the 130 orders can be filled without reordering components? (b) if the manufacturer stocks 132 components, what is the probability that the 130 orders can be filled without reordering components? (c) if the manufacturer stocks 135 components, what is the probability that the 130 orders can be filled without reordering components?