Hatch Enterprises makes backpacks for children and adults from the same nylon ma

Hatch Enterprises makes backpacks for children and adults from the same nylon material.
We receive 5,400 square feet of nylon each week from our supplier. It takes 3 square feet
of nylon to make the adult backpack and 2 square feet to make the child size. We believe
we can sell at most 1,000 adult backpacks per week and at least 750 child size. It takes
45 minutes to sew the adult size and 30 minutes to sew the child size. We have 30 staff
who each work 40 hours per week. We sell the adult backpack for $35 and the child
backpack for $25.
a. Define the decision variables
b. Build the objective function (in standard format)
c. Formulate the constraints
2. Hatch Beverage Company produces high quality apple, strawberry and cranberry juices.
We blend our juices from spring fresh water, sugar and natural flavors. The sales price
per quart of juice is listed below along with the purchase price per unit of ingredient.
Juice Sales Price Ingredient Cost
Apple $7.00 Water $2.00
Strawberry $6.00 Sugar $3.50
Cranberry $5.00 Flavors $4.00
We can purchase up to 10,000 gallons of water and 4,000 pounds of sugar each week.
We need to make at least 3,000 quarts of apple juice, and 2,500 quarts of cranberry juice
each week.
The strawberry juice should be at most 80% water and the cranberry juice should be at
least 10% natural flavors.
How much of each juice should we blend to maximize profits?
a. How many decision variables do we need? Define them.
b. Set up the objective function
c. Define the constraints mathematically
3. Consider the following LP formulation where X1 = tables and X2 = chairs.
Max Z = 3X1 + 3X2
St
4X1 + 5X2 ≤ 40 Wood
2X1 + 6X2 ≤ 24 Metal
3X1 – 3X2 ≥ 6 Plastic
X1 ≥ 4 Demand
a) Solve the problem graphically – shade the feasible region and label the constraints
b) What is the optimal solution?