Maria Salvador, Ltd$.$ produces clothing for the luxury market. The company has only one supplier since they use a special fabric. They have a contract with a company for the whole output $$ a maximum of $7,700$ m$2$ of the fabric per week, at a selling price of $25/$m$2.$ Maria Salvador, Ltd$.$ has the following demand, selling price and costs for its products:

$1.$ Scarves

a$.$ Demand $($units per week$)1,000$

b$.$ Selling price per unit $50$

c$.$ Fabric per unit $($m$2)1$

d$.$ Direct labor hours per unit $0\mathrm{.}25$

e$.$ Packing costs per unit $5$

$2.$ Blouses

a$.$ Demand $($units per week$)2,000$

b$.$ Selling price per unit $90$

c$.$ Fabric per unit $($m$2)2$

d$.$ Direct labor hours per unit $0\mathrm{.}50$

e$.$ Packing costs per unit $7$

$3.$ Skirts

a$.$ Demand $($units per week$)1,500$

b$.$ Selling price per unit $125$

c$.$ Fabric per unit $($m$2)3$

d$.$ Direct labor hours per unit $0\mathrm{.}50$

e$.$ Packing costs per unit $7$

Fixed costs are $22,500$ per week for a five$-$day working week and $400$ direct labor hours per day are available at $10$ per hour.

Question:

Identify the most profitable weekly production plan and compute the profit for that plan.