Giapetto’s Woodcarving Inc. manufactures two types of wooden toys: soldier and trains. A soldier sells for $27 and uses $10 worth of raw materials. Each solider that is manufactured increases Giapetto’s variable labour and overhead costs by $14. A train sells for $21 and uses $9 worth of raw material. Each train built increases Giapetto’s variable labour and overhead costs by $10. The manufacture of wooden soldiers and trains requires two types of skilled labour: carpentry and finishing. A soldier requires 2 hours of finishing labour and 1 hour of carpentry labour. A train requires 1 hour of finishing and 1 hour of carpentry labour. Each week, Giapetto can obtain all the needed raw material but only 100 finishing hours and 80 carpentry hours. Demand for trains is unlimited but at most 40 soldiers are bought each week. Formulate a mathematical method of Giapetto’s situation that can be used to maximize Giapetteo’s weekly profit.
CPI manufactures a standard dining chair used in restaurants. The demand forecasts for chairs for quarter 1 and quarter 2 are 3700 and 4200, respectively. The chair contains an upholstered seat that can be produced by CPI or purchased from DAP. DAP currently charges $12.25 per seat, but has announced a new prices of $13.75 effective the second quarter. CPI can produce at most 3800 seats per quarter at a cost of $10.25 per seat. Seats produced or purchased in quarter 1 can be stored in order to satisfy demand in quarter 2. A seat cost CPI $1.50 each to hold in inventory, and maximum inventory cannot exceed 300 seats. Find the optimal make-or-buy plan for CPI.
The problem is formulated as follows:
X1 = Number of seats produced by CPI in quarter 1.
X2 = Number of seats purchased from DAP in quarter 1.
X3 = Number of seats carried in inventory from quarter 1 to 2.
X4 = Number of seats produced by CPI in quarter 2.
X5 = Number of seats purchased from DAP in quarter 2.