An Entrepreneur Who Operates a Cellular Phone Store Orders Inventory

question 8

Essay

An entrepreneur who operates a cellular phone store orders inventory of cell phones based on four internal memory specifications - 8 GB, 16 GB, 32 GB, and 64 GB. She wants to evaluate her inventory ordering policy for the phones with four different amounts of internal memory. Any phone unsold at the end of a period is kept in inventory for the next sales period and incurs a holding cost expressed as 10% of the cost per unit per period. If demand during a period exceeds supply for a phone, then sale is lost. The data on the cost and selling prices of the cell phones categorized by these memory specifications are known, and representative data on the past sales are also available. $$\begin{array} { | c | c | c | } \hline \text { Internal Memory } & \text { Cost (\$) } & \text { Selling Price (\$) } \\\hline \mathbf { 8 G B } & 420 & 430 \\\mathbf { 1 6 } \mathrm { GB } & 500 & 520 \\\mathbf { 3 2 } \mathrm { GB } & 590 & 620 \\\mathbf { 6 4 } \mathrm { GB } & 670 & 700 \\\hline\end{array}$$ Past Sales: $$\begin{array} { | c | c | c | c | c | } \text { Period } & \mathbf { 8 G B } & \mathbf { 1 6 } \mathbf { G B } & \mathbf { 3 2 } \mathbf { G B } & \mathbf { 6 4 } \mathbf { G B } \\1 & 276 & 274 & 327 & 332 \\2 & 302 & 211 & 264 & 329 \\3 & 299 & 276 & 306 & 239 \\4 & 261 & 258 & 232 & 277 \\5 & 260 & 244 & 278 & 220 \\6 & 306 & 252 & 262 & 252 \\7 & 227 & 213 & 290 & 253 \\8 & 228 & 217 & 308 & 250 \\9 & 205 & 215 & 246 & 277 \\10 & 236 & 237 & 272 & 284 \\11 & 279 & 251 & 301 & 282 \\12 & 303 & 271 & 271 & 282 \\13 & 266 & 252 & 276 & 317 \\14 & 263 & 306 & 285 & 310 \\15 & 210 & 250 & 328 & 253 \\16 & 247 & 230 & 317 & 340 \\17 & 314 & 285 & 289 & 332 \\18 & 283 & 304 & 312 & 256 \\19 & 283 & 245 & 294 & 272 \\20 & 252 & 237 & 262 & 323\end{array}$$
a. Construct a spreadsheet simulation model to estimate the total profit the entrepreneur earns in a period when ordering 300 units of each cell phone. To model the respective cell phone demands, fit a realistic distribution to the sales data. What is the average total profit? What is the estimated likelihood that the entrepreneur makes less than $10,000 next period?
b. Using Spearman rank correlation, compute the correlations between the demands for the cells phones based on the four memory specifications. Incorporate a correlation matrix to captures the interrelationships between the demands for each cell phone type. What is the average total profit? What is the estimated likelihood that the entrepreneur makes less than $10,000 next period? Comparing these answers to (a), conclude how the correlated demand affects the model's implications.

Comprehend the basis of federal legislation’s constitutionality beyond explicitly stated powers in the Constitution.

Recognize the extension of the Fourteenth Amendment's equal protection guarantee to federal government actions through the Fifth Amendment.

Identify the First Amendment’s stance on state regulation of deceptive commercial advertising.

Learn the determination of case types under the jurisdiction of federal courts as specified by Article III of the Constitution.

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Definitions:

Marginal Product

It is the increase in output that results from a one-unit increase in the input, keeping all other inputs constant.

Average Product

The output per unit of a particular input, such as labor or capital, calculated by dividing total product by the quantity of input.

Average Product

The output produced per unit of input used, typically calculated by dividing total product by the quantity of input.

Marginal Product

The additional output gained by employing one more unit of a particular input, keeping other inputs constant.