Question

Louise Mazzone, Production Manager for Stick to Your Knitting Inc., has just signed a contract to supply 1,000 hats and 2,000 scarves to the local Christmas market for $15,000. Each hat requires 50 meters of yarn and each scarf requires 100 meters. She has 50,000 meters of yarn available and an Acme knitting machine which can knit a hat in 8 minutes and a scarf in 10 minutes. 160 machine hours (9,600 minutes) are available. It costs $2 to make a hat and $1.50 to make a scarf. Louise also has the option to subcontract production at a cost of $3 per hat and $2 per scarf.

Here is the formulation of the problem.

Let 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+3BM+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)

Required:
Use Solver on this LP problem to determine the minimum cost of completing the contract.

Answer 1

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