The custom orders division of Philadelphia Engine Company has received a request from Precision Motors for a quotation on an order of 100 long-distance diesel engines for the newest fleet of semi- trucks. Philadelphia Engine has previously only built engines for sedans and SUVs, and thus has never produced the type of long-distance diesel engine that Precision is requesting. However, the engineering department is certain that they can produce an engine that meets the specifications of the order. Philadelphia Engine is unsure of what their exact costs will be, since they have never sourced the parts necessary to build a diesel engine. The production manager at Precision informs Bryce Jones, the head of the custom orders division of the Philadelphia Engine Company that they have also requested a quotation from Baltimore Engine Inc., and that they will purchase all the en- gines in the order from either Philadelphia or Baltimore, meaning no other firm is being considered. Bryce must decide (i) whether or not to bid and (ii) if so, how much their submitted bid should be in order to maximize the firm's expected profit. He knows that there are two uncertain vari- ables to consider: the competing bid from Baltimore Engine Inc. and the production costs that Philadelphia Engine would incur if they produce the diesel engines. Bryce calls his CFO, Annie Thomas, to seek her input about how they should proceed. Annie and Bryce determine that they should consider potential per-engine bids of $3000, $5000, $7000, and potential per-engine production costs of $2000, $4000, and $6000. They examine Bal- timore Engine's public bidding history and believe that they will submit a competing bid of either $4000, $6000, or $8000 for the project. Bryce calls Enrique Santos, the head of the production department, who believes that there is a 50% chance they will be able to use cast iron as the primary base of the engine, meaning they could produce the engine for $4000 each. However, if they instead must use steel, then there is an equal chance of the production costs being $2000 or $6000 depending on the grade of steel that they will need to use. Annie believes there is a 50% chance that Baltimore Engine Inc. will bid at $6000 in line with their recent bidding patterns, but also knows that 35% the time Baltimore Engine bids low to win a contract. This leaves a 15% chance that they bid $8000 for the contract. Knowing these probabilities, Bryce, Annie, and Enrique sit down to make a decision. 1. Draw a decision tree for the decision Philadelphia Engine Company must make. Carefully label the branches and the end payoffs. 2. Determine the expected values for each of the possible decisions, and indicate which decision the company should make in order to maximize expected profit. The custom orders division of Philadelphia Engine Company has received a request from Precision Motors for a quotation on an order of 100 long-distance diesel engines for the newest fleet of semi- trucks. Philadelphia Engine has previously only built engines for sedans and SUVs, and thus has never produced the type of long-distance diesel engine that Precision is requesting. However, the engineering department is certain that they can produce an engine that meets the specifications of the order. Philadelphia Engine is unsure of what their exact costs will be, since they have never sourced the parts necessary to build a diesel engine. The production manager at Precision informs Bryce Jones, the head of the custom orders division of the Philadelphia Engine Company that they have also requested a quotation from Baltimore Engine Inc., and that they will purchase all the en- gines in the order from either Philadelphia or Baltimore, meaning no other firm is being considered. Bryce must decide (i) whether or not to bid and (ii) if so, how much their submitted bid should be in order to maximize the firm's expected profit. He knows that there are two uncertain vari- ables to consider: the competing bid from Baltimore Engine Inc. and the production costs that Philadelphia Engine would incur if they produce the diesel engines. Bryce calls his CFO, Annie Thomas, to seek her input about how they should proceed. Annie and Bryce determine that they should consider potential per-engine bids of $3000, $5000, $7000, and potential per-engine production costs of $2000, $4000, and $6000. They examine Bal- timore Engine's public bidding history and believe that they will submit a competing bid of either $4000, $6000, or $8000 for the project. Bryce calls Enrique Santos, the head of the production department, who believes that there is a 50% chance they will be able to use cast iron as the primary base of the engine, meaning they could produce the engine for $4000 each. However, if they instead must use steel, then there is an equal chance of the production costs being $2000 or $6000 depending on the grade of steel that they will need to use. Annie believes there is a 50% chance that Baltimore Engine Inc. will bid at $6000 in line with their recent bidding patterns, but also knows that 35% the time Baltimore Engine bids low to win a contract. This leaves a 15% chance that they bid $8000 for the contract. Knowing these probabilities, Bryce, Annie, and Enrique sit down to make a decision. 1. Draw a decision tree for the decision Philadelphia Engine Company must make. Carefully label the branches and the end payoffs. 2. Determine the expected values for each of the possible decisions, and indicate which decision the company should make in order to maximize expected profit