Question: if the product mix remains constant, what will the breakeven number of pairs of sandals for each of the three products be?

Please show full calculations with full explanations.

Sea Brink Sandals Sea Brink Sandals (SBS) produces three types of sandals, the Active, the Beach, and the Coral. SBS sells the sandals to sportswear and beach stores in the South of France. The owner of SBS, Georgette, launched SBS after years of frustration with the poor quality of beach footwear. Georgette is very proud to do business with local artisans who use sustainable materials. Since its creation 10 years before, SBS has become a staple renowned in the South of France, and Georgette is dreaming to expand the company in other markets. The following information is for next year's production and sales. SBS plans to make and sell a total of 53,000 pairs of sandals next year. The production plan broken down by product is: 20,000 pairs of Active, 18,000 pairs of Beach, and 15,000 pairs of Coral. SBS's accountant Pierre determined that maximum demand from the French market next year will be 22,000 Active, 20,000 Beach, and 20,000 Coral. The selling price per pair of sandals will be $18 for Active, $22 for Beach, and $24 for Coral. The production process at SBS is a bit particular. To make any type of pairs of sandals (Active, Beach or Coral), SBS must first make a pair of Active. It means that the Active product is used as the underlying product for the two other products, Beach and Coral. To make a Beach or Coral pair, SBS first makes a pair of Active and then transforms it into a pair of either Beach or Coral. The direct material cost per Active pair will be $7. The direct labour hourly wage will be $28. Direct labour will be able to make 10 Active pairs per direct labour hour. The production supervisor dedicated to the production of the Active sandals will receive a $62,000 yearly salary. To make the Beach and Coral sandals, SBS adds more direct materials to the underlying product (the Active product): a pair of Beach will require an additional $4 in direct materials compared to its underlying product Active, while the additional direct materials cost for a pair of Coral will be $1.50. Moreover, the transformation process of Active into the two other products takes additional labour time that is paid at the same hourly rate. Once the Active pair will be made, the Beach pair will need an additional 0.025 direct labour hours, and the Coral pair will need an additional 0.060 direct labour hours to be finished. The salary of the supervisors in charge of the production of the Beach and Coral products will be $62,000 and $62,000 respectively. The yearly salaries of the production supervisors will be identical whichever the product in the current plan, and they are specific to their respective product. Pierre has also estimated the following corporate fixed costs for next year. SBS will rent its current building for $6,000 per month. Planned selling and administrative expenses will be $90,000. Depreciation will be $70,000. Finally, production capacity is limited by the number of direct labour hours. The company plans to operate at practical capacity next year, which the current production plan reflects. SBS operates in just in time, meaning that they do not keep any inventory of materials, work-in-process units, or completed units. maro Sea Brink Sandals Sea Brink Sandals (SBS) produces three types of sandals, the Active, the Beach, and the Coral. SBS sells the sandals to sportswear and beach stores in the South of France. The owner of SBS, Georgette, launched SBS after years of frustration with the poor quality of beach footwear. Georgette is very proud to do business with local artisans who use sustainable materials. Since its creation 10 years before, SBS has become a staple renowned in the South of France, and Georgette is dreaming to expand the company in other markets. The following information is for next year's production and sales. SBS plans to make and sell a total of 53,000 pairs of sandals next year. The production plan broken down by product is: 20,000 pairs of Active, 18,000 pairs of Beach, and 15,000 pairs of Coral. SBS's accountant Pierre determined that maximum demand from the French market next year will be 22,000 Active, 20,000 Beach, and 20,000 Coral. The selling price per pair of sandals will be $18 for Active, $22 for Beach, and $24 for Coral. The production process at SBS is a bit particular. To make any type of pairs of sandals (Active, Beach or Coral), SBS must first make a pair of Active. It means that the Active product is used as the underlying product for the two other products, Beach and Coral. To make a Beach or Coral pair, SBS first makes a pair of Active and then transforms it into a pair of either Beach or Coral. The direct material cost per Active pair will be $7. The direct labour hourly wage will be $28. Direct labour will be able to make 10 Active pairs per direct labour hour. The production supervisor dedicated to the production of the Active sandals will receive a $62,000 yearly salary. To make the Beach and Coral sandals, SBS adds more direct materials to the underlying product (the Active product): a pair of Beach will require an additional $4 in direct materials compared to its underlying product Active, while the additional direct materials cost for a pair of Coral will be $1.50. Moreover, the transformation process of Active into the two other products takes additional labour time that is paid at the same hourly rate. Once the Active pair will be made, the Beach pair will need an additional 0.025 direct labour hours, and the Coral pair will need an additional 0.060 direct labour hours to be finished. The salary of the supervisors in charge of the production of the Beach and Coral products will be $62,000 and $62,000 respectively. The yearly salaries of the production supervisors will be identical whichever the product in the current plan, and they are specific to their respective product. Pierre has also estimated the following corporate fixed costs for next year. SBS will rent its current building for $6,000 per month. Planned selling and administrative expenses will be $90,000. Depreciation will be $70,000. Finally, production capacity is limited by the number of direct labour hours. The company plans to operate at practical capacity next year, which the current production plan reflects. SBS operates in just in time, meaning that they do not keep any inventory of materials, work-in-process units, or completed units. maro