Princetown paints ltd manufactures three basic types of paint. emulsion, gloss, and undercoat. using the same mixing machines and direct labour for each of the three products. the Management accountant of Princetown paints was faced with the task of arranging the weekly production for his company. information about the sale price and costs per 100 liters is given in the following table ( all figures in $). sales price per 100 liters ( emulsion 120), ( gloss 126), ( undercoat 110). variable cost per 100 liters ( emulsion 120), ( gloss 126), ( undercoat 110). direct material costs ( emulsion 11), ( gloss 25), ( undercoat 20). direct labour costs ( emulsion 30), ( gloss 36), ( undercoat 24). mixing costs ( emulsion 32), ( gloss 20), ( undercoat 36). other variable costs ( emulsion 12), ( gloss 15), ( undercoat 10). the cost of direct labour is $3 per hour and the variable cost of mixing is $4 per hour. in any one week, direct labour hours are restricted to 8000 hours and mixing machine hours are restricted to 5900 hours. due to contractual arrangements the company must produce exactly 25,000 liters of undercoat each week. there is a maximum weekly demand for emulsion paint of 35,000 litres and for gloss paint of 29,000 liters. (a) formulate the linear programming problem to determine the weekly production levels for emulsion and gloss paint that maximize contribution to profit. (b) solve the problem graphically. state the optimum weekly production levels and the corresponding contribution to profit. (c) calculate by how much the sales price of emulsion paint must change from its current level before the optimal solution will change. (d) suppose that the labour force is prepared to work overtime at a premium of $1 per overtime hour worked. would it be profitable to work overtime? if so , how many hours would you recommend should be worked, and what would be the extra profit from these hours? QUESTION ONEPrincetown Paints Ltd manufactures three basic types of paint-emulsion, gloss and undercoat-us-ing the same mixing machines and direct labour for each of the three products. The managementaccountant of Princetown Paints was faced with the task of arranging the weekly production for hiscompany. Information about the sales price and costs per 100 litres is given in the following table (allfigures in £).Sales price (per 100 litres)Variable costs (per 100 litres):Direct material costsDirect labour costsMixing costsOther variable costsEmulsion12011303212Gloss12625362015Undercoat11020243610The cost of direct labour is £3 per hour and the variable cost of mixing is £4 per hour. In any oneweek, direct labour hours are restricted to 8000 hours and mixing machine hours are restricted to5900 hours.Due to contractual arrangements the company must produce exactly 25,000 litres of undercoateach week. There is a maximum weekly demand for emulsion paint of 35,000 litres and for gloss paintof 29,000 litres.Required:Formulate the linear programming problem to determine the weekly production levels foremulsion and gloss paint that maximise contribution to profit.Solve the problem graphically. State the optimum weekly production levels and the correspond-ing contribution to profit.(C) Calculate by how much the sales price of emulsion paint must change from its current levelbefore the optimal solution will change.Suppose that the labour force is prepared to work overtime at a premium of £l per overtimehour worked. Would it be profitable to work overtime? If so, how many hours would yourecommend should be worked, and what would be the extra profit from these hours?

Question

Princetown paints ltd manufactures three basic types of paint. emulsion,  gloss, and undercoat. using the same mixing machines and direct labour for each of the three products. the Management accountant of Princetown paints was faced with the task of arranging the weekly production for his company. information about the sale price and costs per 100 liters is given in the following table ( all figures in $). sales price per 100 liters ( emulsion 120), ( gloss 126), ( undercoat 110). variable cost per 100 liters ( emulsion 120), ( gloss 126), ( undercoat 110). direct material costs ( emulsion 11), ( gloss 25), ( undercoat 20). direct labour costs ( emulsion 30), ( gloss 36), ( undercoat 24). mixing costs ( emulsion 32), ( gloss 20), ( undercoat 36). other variable costs ( emulsion 12), ( gloss 15), ( undercoat 10). the cost of direct labour is $3 per hour and the variable cost of mixing is $4 per hour. in any one week, direct labour hours are restricted to 8000 hours and mixing machine hours are restricted to 5900 hours. due to contractual arrangements the company must produce exactly 25,000 liters of undercoat each week. there is a maximum weekly demand for emulsion paint of 35,000 litres and for gloss paint of 29,000 liters. (a) formulate the linear programming problem to determine the weekly production levels for emulsion and gloss paint that maximize contribution to profit. (b) solve the problem graphically. state the optimum weekly production levels and the corresponding contribution to profit. (c) calculate by how much the sales price of emulsion paint must change from its current level before the optimal solution will change. (d) suppose that the labour force is prepared to work overtime at a premium of $1 per overtime hour worked. would it be profitable to work overtime? if so , how many hours would you recommend should be worked, and what would be the extra profit from these hours? QUESTION ONEPrincetown Paints Ltd manufactures three basic types of paint-emulsion, gloss and undercoat-us-ing the same mixing machines and direct labour for each of the three products. The managementaccountant of Princetown Paints was faced with the task of arranging the weekly production for hiscompany. Information about the sales price and costs per 100 litres is given in the following table (allfigures in £).Sales price (per 100 litres)Variable costs (per 100 litres):Direct material costsDirect labour costsMixing costsOther variable costsEmulsion12011303212Gloss12625362015Undercoat11020243610The cost of direct labour is £3 per hour and the variable cost of mixing is £4 per hour. In any oneweek, direct labour hours are restricted to 8000 hours and mixing machine hours are restricted to5900 hours.Due to contractual arrangements the company must produce exactly 25,000 litres of undercoateach week. There is a maximum weekly demand for emulsion paint of 35,000 litres and for gloss paintof 29,000 litres.Required:Formulate the linear programming problem to determine the weekly production levels foremulsion and gloss paint that maximise contribution to profit.Solve the problem graphically. State the optimum weekly production levels and the correspond-ing contribution to profit.(C) Calculate by how much the sales price of emulsion paint must change from its current levelbefore the optimal solution will change.Suppose that the labour force is prepared to work overtime at a premium of £l per overtimehour worked. Would it be profitable to work overtime? If so, how many hours would yourecommend should be worked, and what would be the extra profit from these hours?

Accepted Answer

Answered: Image /qna-images/answer/8322d66f-2a03-49a3-a2dc-14c8952733d9.jpg