I needs some help with the following problems. Especially on the constraint of at least 4 children's app must be launched. Thank you

Refer to the Par Insights, Inc. example in your textbook. A competitor firm DLS Apps, Inc. decides to enter the market for apps made for teenagers and children. Their Production Supervisor analyzed each of the operations and concluded that if the company produces apps for children, cach app would require 7 hours in the theme creation department, 11 hours in the graphics and imaging department, 4 hours in the educational content department, 7 hours in the coding department, and 4 hours in the testing and launching department. On the other hand, each app for teenagers would require 6 hours in the theme creation department, 14 hours in the graphics and imaging department, 12 hours in the educational content department, 10 hours in the coding department, and 1 hour in the testing and launching department. After studying the departmental workload projections, the Production Supervisor estimates that 100 hours for theme creation, 250 hours for graphics and imaging, 200 hours for the educational content creation, 150 hours of coding and 50 hours for the testing and launching are available for the production of the new apps during the next four months. The accounting department analyzed the costs based on the production data and overheads and arrived at prices for the apps that will result in a profit contribution of $12,000 per children's app and $16,000 per teenager app produced. The CEO asserts that to be successful in the long run, at least 4 children's apps must be launched in the next four months. The management is trying to identify how many apps of each type should they launch in the next four months and have hired you to help them figure out what the optimal solution would be and what the expected profits would be. Obtain the optimal solution, either graphically or by using Excel Solver (You'll be uploading this file in a later question). Fill in the following blanks based on your solution: a. The total expected profit is $ b. They should make Children's apps and Teenager's Apps. c. The department has the highest slack of hours d. If the company was able to obtain 5 more hours in the Theme department, the profit would increase by $ (round it up to the nearest whole number)