Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets 5th Editi

              c)    $1,333.33


1.5         a)   

              b)    Break-even point = ($10,000,000) / ($1700 – $1300) = 25,000.
              c)    Maximize Profit = $0 {if Q = 0} and –$10,000,000 + $400Q {if Q > 0}
subject to 0 ≤ Q ≤ s.
              d)   

              e)   



1.6         a)    Jennifer must decide how much to ship from each plant (A and B) to each retail outlet (1 and 2). Let xˆj = amount to ship from plant i (for i = A, B) to each retail outlet j (for j = 1, 2).
              b)    Shipping Cost = $700xA1 + $400xA2 + $800xB1 + $600xB2
              c)    xA1 + xA2 = 30;  xB1 + xB2 ≤ 500;  xA1 + xB1 = 40;  xA2 + xB2 ≥ 25;  all xij ≥ 0.
              d)    Minimize Shipping Cost = $700xA1 + $400xA2 + $800xB1 + $600xB2
subject to
           xA1 + xA2 = 30
           xB1 + xB2 ≤ 500
           xA1 + xB1 = 40
           xA2 + xB2 ≥ 25
and
           all xij ≥ 0
              e)    Jennifer should ship all of Retail Outlet 2’s 25 units from Plant A because it is $200 cheaper than from Plant B. Retail Outlet 1 should get all it can from Plant A (5 units) because it is $100 cheaper than from Plant B. The remaining 35 units should come from Plant B. The decision variables would be xA1 = 5, xA2 = 25, xB1 = 35, xB2 = 0.
1.7         a)

They should produce the motors internally.
              b)    Break-even point = $1,000,000 / ($2,000 - $1,600) = 2,500.
1.8         a)   

              b)    The make option appears to be better ($20,000,000 profit for the make option vs. $17,500,000 profit for the buy option).

              c)    Q = number of watches to produce for sale.
Make Option: Profit = $0 {if Q = 0} and –$10,000,000 + $1,000Q {if Q > 0}.
Buy Option: Profit = $0 {if Q = 0} and –$5,000,000 + $750Q {if Q > 0}.

Incremental profit from choosing make option rather than buy option