Answer:
the optimal solution was to manufacture 1,000 hats and subcontract the production of 2,000 scarves.
total cost = (1,000 x $2) + (2,000 x $2) = $2,000 + $4,000 = $6,000
Step-by-step explanation:
MH be the number of hats made.
Let MS be the number of scarves made.
Let BH be the number of hats bought.
Let BS be the number of scarves bought.
Minimize Cost: 2MH + 1.5MS + 3BH +2BS
subject to
- 50MH+100MS ≤ 50,000 (Available Yarn)
- 8MH+10MS ≤ 9,600 (Machine Time)
- MH+BH ≥1,000 (Hats Needed)
- MS+BS ≥ 2,000 (Scarves Needed)
- MH,MS,BH, BS ≥ 0 (Non-negativity)
We are given all the constraints and the cost minimizing equation, therefore, all we need to do is plug the numbers into solver (excel function);
the optimal solution was to manufacture 1,000 hats and subcontract the production of 2,000 scarves.
total cost = (1,000 x $2) + (2,000 x $2) = $2,000 + $4,000 = $6,000