Exam 1: Introduction to Management Science, Modeling, and Excel Spreadsheets

A plant producing hydrogen has a fixed overhead of $\$ 10,000,000$ per year and incurs a variable cost of $\$ 40.00$ per ton. The average selling price is $\$ 90.00$ per ton. (A) What is the breakeven volume for this plant? (B) What is the total sales revenue that will produce a net contribution of $\$ 2,000,000$ ? (C) What is the number of units produced by the plant in 2004, if its net contribution during 2004 is $\$ 3,000,000$ ? (D) If production is 250,000 tons in 2003 and 150,000 tons in 2003, what is the net contribution during 2002 and 2003 combined?

Kathy Smith works for a cell phone company. She is paid $\$ 3.00$ per hour (note that commission sales personnel may be paid less than the minimum wage) plus a commission of $\$ 20.00$ per phone sold. Kathy works for 40 hours a week. The company sells the phones for $\$ 100$ a phone and buys it for $\$ 40.00$ per phone. The company hopes to sell anywhere from 10 to 60 phones per week. From the company's point of view, considering Kathy's wages and phone costs as the only expenses related to cell phone sales, the fixed cost per week is

A one-machine shop producing bolts has a fixed cost of $\$ 2,000.00$ and a variable cost of $\$ 2.00$ per bolt. The selling price is $\$ 6.00$ per unit. Net profit corresponding to the breakeven volume of production is

An insurance salesperson is paid $\$ 6.00$ an hour and a commission of $\$ 1.50$ per $\$ 1,000$ of insurance sold. The firm sells each $\$ 1,000$ of insurance for $\$ 20.00$ . (A) If each salesman works for exactly 40 hours per week, and if the total compensation received by the 10 salesmen working for this firm during a typical week is $\$ 18,900$ , what is the total value of insurance sold during a typical week? (B) If the firm changes the compensation package to $\$ 20.00$ per hour and a commission of $\$ 0.25$ per $\$ 1000$ of insurance sold, what will be the total compensation for a typical week? (C) For a single salesman, what will be the volume of sales needed to make a wage of $\$ 2,010$ per week?

Demand for a product follows normal distribution (one of many statistical distributions you learned earlier). Models using this data are best done using

Mathematical models usually contain

Kathy Smith works for a cell phone company. She is paid $\$ 3.00$ per hour (note that commission sales personnel may be paid less than the minimum wage) plus a commission of $\$ 20.00$ per phone sold. Kathy works for 40 hours a week. The company sells the phones for $\$ 100$ a phone and buys it for $\$ 40.00$ per phone. The company hopes to sell anywhere from 10 to 60 phones per week. From the company's point of view, considering Kathy's wages and phone costs as the only expenses related to cell phone sales, the breakeven sales volume is

Two of the steps in the management science approach to problem solving are

Kathy Smith works for a cell phone company. She is paid $\$ 3.00$ per hour (note that commission sales personnel may be paid less than the minimum wage) plus a commission of $\$ 20.00$ per phone sold. Kathy works for 40 hours a week. The company sells the phones for $\$ 100$ a phone and buys it for $\$ 40.00$ per phone. The company hopes to sell anywhere from 10 to 60 phones per week. From the company's point of view, considering Kathy's wages and phone costs as the only expenses related to cell phone, net contribution for a sales level of 50 phones is

A one person automobile oil change in rural Mississippi has a fixed overhead of $\$ 900.00$ per month. The variable cost per oil change $\$ 10.00$ . The charge is $\$ 30.00$ for one oil change. If the owner/worker Joe Smith performed 300 oil changes in November 2005; total sales revenue for November 2005 is

A deterministic model would be appropriate to use if the

You are trying to lease a gasoline-powered car or a hybrid car based on cost considerations during the next 5 years that you plan to keep it. You plan to drive 12,000 miles per year. Ignore the effect of interest rates and time value of money. Leasing cost is $\$ 250$ per month for the gas-powered car and $\$ 350$ per month for the hybrid. Down payment is $\$ 0$ for both cars. 12,000 leasing miles are allowed per year for each car. Per mile charge for gas-powered cars is $\$ 0.15$ and $\$ 0.05$ for hybrids. Which would be a better buy, from a cost minimization point of view?

A company sets up elderly clients for general purpose household software, such as Quicken, for a flat fee through its agents. Agents are paid a retention fee of $\$ 600.00$ per week and a flat fee of $\$ 100$ per setup. The software itself costs $\$ 100.00$ per unit; the total charge per installation is $\$ 350$ . (A) What sales volume per week will make the firm break even? (B) How many installations per week should be targeted if the target profit is $\$ 3900.00$ per week? (C) If Joe Jackson, a Detroit-based salesman, installs the software for 500 clients during the first week of March 2006, what will be his commission for that week? (D) If Joe Jackson, a Detroit-based salesman installs the software for 500 clients during the first week of March 2006, what will the firm earn (net contribution) through its association with Joe Jackson?

Probabilistic model would be appropriate to use if the

Benefits of model building include

You are trying to lease a gasoline-powered car or a hybrid car based on cost considerations during the next 5 years that you plan to keep it. You plan to drive 12,000 miles per year. Ignore the effect of interest rates and time value of money. Leasing cost is $\$ 250$ per month for the gas-powered car and $\$ 325$ per month for the hybrid. Down payment is $\$ 0$ for both cars. 12,000 leasing miles are allowed per year for each car. Per mile charge for gas powered cars is $\$ 0.15$ and $\$ 0.05$ for hybrids. Which would be a better buy, from a cost minimization point of view?

Demand for a product is 10,000 per month for sure and the variable and fixed costs are also known with a high level of certainty. Models incorporating this data are best done using

A one-person automobile oil change in rural Mississippi has a fixed overhead of $\$ 900.00$ per month. The variable cost per oil change $\$ 10.00$ . The charge is $\$ 30.00$ for one oil change. If the owner/worker Joe Smith performed 200 oil changes in October 2005, the total contribution in October 2005 is

There are two machines available in the market for making frozen pancakes. Machine A incurs a fixed cost of $\$ 10,000$ per year and a variable cost of $\$ 0.03$ per pancake. Machine B incurs a fixed cost of $\$ 30,000$ per year and a variable cost of $\$ 0.01$ per pancake. The selling price is $\$ 0.05$ per pancake. (A) If the expected sales volume per year is 600,000 , which machine will give higher net contribution? (B) If the expected sales volume per year is 1,000,000, which machine will give higher net contribution? (C) What is the breakeven volume of Machine A?

A one-machine shop producing bolts has a fixed cost of $\$ 2,000.00$ and a variable cost of $\$ 2.00$ per bolt. The selling price is $\$ 6.00$ per unit. The breakeven volume of production is