Adrian Bicycle Company (ABC) has the hottest new products on the upscale toy market for boys and girls bikes in bright fashion colors, with over sized hubs and axles, shell design safety tires, a strong padded frame,-chrome plaited chains,brackets and valves, and a non slip handlebar.Due to the sellers market for high quality toys for the newest baby boomers,ABC can sell all the bicycles it manufactures at the following prices: boys bikes P220,girls bikes-P175. This is the price payable to ABC at its Francistown plant.The firms accountant has determined that direct labor costs will be 45% of the price ABC receives for the boys model and 40% for the price received for the girls model.Production costs other than labor, but excluding painting and packaging, are P44 per boys bicycle and P30 per girls bicycle. Painting and packaging are P20 per bike, regardless of model.The Francistown plants overall production capacity is 390 bicycles per day. At least 100 boys bicycles should be produced per day and not more than 250 girlsbikes should be produced per day. Each boys bike requires 3.00 labor hours and each girls model, 1.5 hours, to complete. ABC currently employs 120 workers,who each put in an eight hour day. The firm has no desire to hire or fire to affect labor availability, for it believes its stable workforce is one of its biggest assets.

a) Formulate a linear program model for ABC Company. (10 Marks)

b) Present graphical solution of the ABCs problem (computer output). (5 Marks)

c) Determine from the computer output the number of boys and girls bikes ABC must produce to maximize profit contribution? (5 Marks)

d) Will your recommendation be affected if the selling price per boys bike goes up by P10? (i.e. Calculate the range of optimality for this model and interpret it) (5 Marks)

e)Will your recommendation be affected if the selling price per girls bike goes up by P5? (i.e. Calculate the range of optimality for this model and interpret it) (5 Marks)