A workshop has 5 jobs to perform today. Each job must be done by exactly one machine, but a machine can do more than one job. For each machine, there is a setup cost for the regular workday. Once this cost is paid, you can use the machine for up to 8 hours; if you do not pay the setup cost, you cannot use the machine today. If you set up a machine for the regular workday, you may also elect to set up the machine for overtime, in which case there is an additional cost and you may use the machine for up to 2 more hours. On the other hand, if you do not set up a machine for the regular workday, it cannot be used for overtime. The costs are as follows:

Setup Cost Overtime Cost
Machine 1 600 190
Machine 2 700 200
Machine 3 550 275
Machine 4 675 150
Machine 5 585 195
Thus, if you pay $600, you can use machine 1 for up to 8 hours, and if you pay $600 + $190 = $790, you may use machine 1 for up to 8 + 2 = 10 hours. The number of hours each job takes on each machine is as follows:

Job 1 Job 2 Job 3 Job 4 Job 5
Machine 1 3.0 4.0 5.5 2.5 3.1
Machine 2 3.8 4.9 6.4 2.9 2.7
Machine 3 3.6 4.8 5.5 3.8 2.8
Machine 4 2.9 5.3 5.6 2.9 1.9
Machine 5 3.1 6.0 5.1 2.6 2.5

Define the decision variables

Alandowner entered into a written agreement with a real estate broker whereby the broker would receive a commission of 10% of the sale price if he procured a "ready, willing, and able buyer" for the landowner's property and if the sale actually proceeded through closing. the broker found a buyer who agreed in writing to buy the property from the landowner for $100,000, the landowner's asking price. the buyer put up $6,000 as a down payment. the agreement between the landowner and the buyer contained a liquidated damages clause providing that, if the buyer defaulted by failing to tender the balance due of $94,000 at the closing date, damages would be 10% of the purchase price. the landowner included that clause because she was counting on using the proceeds of the sale for a business venture that would likely net her at least $10,000. the buyer became seriously ill and defaulted. when he recovered, he demanded that the landowner return his $6,000, and the landowner refused. the broker also demanded the $6,000 from the landowner and was refused. the broker and the buyer filed separate suits against the landowner, with the buyer pleading impossibility of performance. the two cases are consolidated into a single case. how should the court rule as to the disposition of the $6,000?

Problem page a medical equipment industry manufactures x-ray machines. the unit cost c (the cost in dollars to make each x-ray machine) depends on the number of machines made. if x machines are made, then the unit cost is given by the function =cx+−0.3x2126x31,935 . how many machines must be made to minimize the unit cost?

Suppose that fizzo and pop hop are the only two firms that sell orange soda. the following payoff matrix shows the profit (in millions of dollars) each company will earn depending on whether or not it advertises: pop hopadvertise doesn’t advertisefizzo advertise 10, 10 18, 2doesn’t advertise 2, 18 11, 11for example, the upper right cell shows that if fizzo advertises and pop hop doesn't advertise, fizzo will make a profit of $18 million, and pop hop will make a profit of $2 million. assume this is a simultaneous game and that fizzo and pop hop are both profit-maximizing firms. if fizzo decides to advertise, it will earn a profit if pop hop advertises and a profit if pop hop does not advertise. if fizzo decides not to advertise, it will earn a profit if pop hop advertises and a profit if pop hop does not advertise. if pop hop advertises, fizzo makes a higher profit if it chooses (not to advertise, to .if pop hop doesn't advertise, fizzo makes a higher profit if it chooses (not to advertise, to . suppose that both firms start off not advertising. if the firms act independently, what strategies will they end up choosing? fizzo will choose to advertise and pop hop will choose not to advertise. both firms will choose to advertise. fizzo will choose not to advertise and pop hop will choose to advertise. both firms will choose not to advertise. again, suppose that both firms start off not advertising. if the firms decide to collude, what strategies will they end up choosing? fizzo will choose not to advertise and pop hop will choose to advertise. both firms will choose not to advertise. fizzo will choose to advertise and pop hop will choose not to advertise. both firms will choose to advertise.