Question

production: The Bronze Forge produces and ships three different hand-crafted bronze plates: a dogwood-engraved cake plate, a wheat-engraved bread plate, and a lace-engraved dinner plate. Each cake plate requires $15 in materials, 5 hours in labor, and $6 to ship. Each bread plate requires $10 in materials, 4 hours of labor, and $5 to ship. Each dinner plate requires $8 in materials, 4 hours in labor, and $5 to deliver. The profit on the cake plate is $15, on the bread plate is $12, and on the dinner plate is $5. The company has available up to 2700 hours of labor per week. Each week they can spend at most $1500 on materials and $1200 on delivery. How many of each plate should the company produce to maximize their weekly profit? What is their weekly profit?

Answer 1

Dogwood- wheat- lace- engraved engraved engraved cake plate bread plate dinner plate $10 $8 5 Hrs 4 Hrs 4 Hrs $6 $15 $12 5 Material price per plate Labor hours per plate Shipping cost per plate Profit per plate $15 $5 Maximum spend on Materials per week Maximum Labour hours per week Maximum spend on Shipping cost per week $1.500 2700 Hrs $1,200

Dogwood- wheat- lace- engraved engraved engraved cake plate bread plate dinner plate Maximum production of Plates: Based on Material ($1,500 / Material price per plate) Based on Labor (2.700 Hours / Labou hours per plate) Based on Ship ($1,200 / Shipping cost per plate) 100 plates 150 plates 540 plates 675 plates 200 plates 240 plates 187.5 plates 675 plates 240 plates Hence, the maximum plates that we can produce is Profit per unit Total Profit 100 plates $15 $1,500 150 plates $12 $1,800 187.5 plates $5 $937.5 The company should produce 150 plates of "wheat-engraved bread" to maximize the weekly profit as it gives the highest profit. Hence, the weekly profit is $1,800 (by producing 150 plates of 150 plates of wheat-engraved bread.)