MegaSports, Inc. produces two high-priced metal baseball bats, the Slugger and the Launcher, that are made...

MegaSports, Inc. produces two high-priced metal baseball bats, the Slugger and the Launcher, that are made from special aluminum and steel alloys. The cost to produce a Slugger bat is $100, and the cost to produce a Launcher bat is $120. We cannot assume that MegaSports will sell all the bats it can produce. As the selling price of each bat model—Slugger and Launcher—increases, the quantity demanded for each model goes down.

Assume that the demand, S, for Slugger bats is given by S = 640 − 4PS and the demand, L, for Launcher bats is given by L = 450 − 3 PL where PS is the price of a Slugger bat and PL is the price of a Launcher bat. MegaSports manufactures as many bats as there is demand for at the price it charges for them.

Q3: (2pts) What are the optimal number of Slugger bats and Launcher bats manufactured if there is no constraint and you want to maximize profit?

Q4: (3pts) The Slugger uses 2 units of special alloys in its manufacture and the Launcher uses 1 unit. You currently have (at most) 200 units of special alloys available. Write the constrained problem. Is the point you found in Q3 feasible for the constrained problem? Plot the feasible set and objective function lines around the point you found in Q3. Which constraint is tight at optimality?

Solutions

Expert Solution

Q3. Optimal number of bats manufactured if there is no constrains and maximizing Profit:

1. Slugger Bats: 120

2. Launcher Bats : 45

Formula for Cell D2 : =640-4*C2

Formula for Cell D3 : =450-3*C3

Formula for Cell E2 : =(C2-B2)*D2

Formula for Cell E3 : =(C3-B3)*D3

Formula for Cell E4 : =SUM(E2:E3)

Solver constraints:

Q4. No , the point found in Q3 is not feasible with Constraints. With the constraint, demand for Slugger bat is 84 and for Launcher bat is 32 (rounding to the nearest integer)

Formula for F2: =2*D2

Formula for F3: =2*D3

Solver Parameters:

keosha answered 2 years ago

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